{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Gaussian Processes (GP) with GPy\n",
    "\n",
    "We will use GPy library for GP modeling [SheffieldML github page](https://github.com/SheffieldML/GPy).\n",
    "\n",
    "Why **GPy**?\n",
    "\n",
    "* Specialized library of GP models (regression, classification, GPLVM)\n",
    "* Variety of covariance functions is implemented\n",
    "* There are GP models for large-scale problems\n",
    "* Easy to use"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Uncomment and run the following line to install GPy library"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "!pip install GPy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "from __future__ import print_function\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import GPy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Current documentation of GPy library can be found [here](http://gpy.readthedocs.org/en/latest/)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Gaussian Process Regression\n",
    "\n",
    "A data set $\\left (X, \\mathbf{y} \\right ) = \\left \\{ (x_i, y_i), x_i \\in \\mathbb{R}^d, y_i \\in \\mathbb{R} \\right \\}_{i = 1}^N$ is given.  \n",
    "\n",
    "Assumption:\n",
    "$$\n",
    "y = f(x) + \\varepsilon,\n",
    "$$\n",
    "where $f(x)$ is a Gaussian Processes and $\\varepsilon \\sim \\mathcal{N}(0, \\sigma_n^2)$ is a Gaussian noise ."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Posterior distribution\n",
    "$$\n",
    "y_* | X, \\mathbf{y}, x_* \\sim \\mathcal{N}(m(x_*), \\sigma(x_*)),\n",
    "$$\n",
    "with predictive mean and variance given by\n",
    "$$\n",
    "m(x_*) = \\mathbf{k}^T \\mathbf{K}_y^{-1} \\mathbf{y} = \\sum_{i = 1}^N \\alpha_i k(x_*, x_i),\n",
    "$$\n",
    "$$\n",
    "\\sigma^2(x_*) = k(x_*, x_*) - \\mathbf{k}^T\\mathbf{K}_y^{-1}\\mathbf{k},\n",
    "$$\n",
    "where\n",
    "$$\n",
    "\\mathbf{k} = \\left ( k(x_*, x_1), \\ldots, k(x_*, x_N) \\right )^T\n",
    "$$\n",
    "$$\n",
    "\\mathbf{K}_y = \\|k(x_i, x_j)\\|_{i, j = 1}^N + \\sigma_n^2 \\mathbf{I}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Building GPR model\n",
    "\n",
    "Lets fit GPR model for function $f(x) = − \\cos(\\pi x) + \\sin(4\\pi x)$ in $[0, 1]$,\n",
    "with noise $y(x) = f(x) + \\epsilon$, $\\epsilon \\sim \\mathcal{N}(0, 0.1)$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1c2774b518>]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 10\n",
    "X = np.linspace(0.05, 0.95, N).reshape(-1, 1)\n",
    "Y = -np.cos(np.pi * X) + np.sin(4 * np.pi * X) + \\\n",
    "    np.random.normal(loc=0.0, scale=0.1, size=(N, 1))\n",
    "plt.figure(figsize=(5, 3))\n",
    "plt.plot(X, Y, '.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### 1. Define covariance function\n",
    "\n",
    "The most popular kernel - RBF kernel - has 2 parameters: `variance` and `lengthscale`, $k(x, y) = \\sigma^2 \\exp\\left ( -\\dfrac{\\|x - y\\|^2}{2l^2}\\right )$,\n",
    "where `variance` is $\\sigma^2$, and `lengthscale` - $l$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "input_dim = 1\n",
    "variance = 1\n",
    "lengthscale = 0.2\n",
    "kernel = GPy.kern.RBF(input_dim, variance=variance,\n",
    "                      lengthscale=lengthscale)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### 2. Create GPR model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Name : GP regression\n",
      "Objective : 13.214582411688195\n",
      "Number of Parameters : 3\n",
      "Number of Optimization Parameters : 3\n",
      "Updates : True\n",
      "Parameters:\n",
      "  \u001b[1mGP_regression.         \u001b[0;0m  |  value  |  constraints  |  priors\n",
      "  \u001b[1mrbf.variance           \u001b[0;0m  |    1.0  |      +ve      |        \n",
      "  \u001b[1mrbf.lengthscale        \u001b[0;0m  |    0.2  |      +ve      |        \n",
      "  \u001b[1mGaussian_noise.variance\u001b[0;0m  |    1.0  |      +ve      |        \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f1c276b24e0>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " /home/yeahrmek/miniconda3/lib/python3.6/site-packages/matplotlib/figure.py:2267: UserWarning:This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = GPy.models.GPRegression(X, Y, kernel)\n",
    "print(model)\n",
    "model.plot(figsize=(5, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Parameters of the covariance function\n",
    "\n",
    "Values of parameters of covariance function can be set like:  `k.lengthscale = 0.1`.\n",
    "\n",
    "Let's change the value of `lengthscale` parameter and see how it changes the covariance function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k = GPy.kern.RBF(1)\n",
    "theta = np.asarray([0.2, 0.5, 1, 2, 4, 10])\n",
    "figure, axes = plt.subplots(2, 3, figsize=(8, 4))\n",
    "for t, ax in zip(theta, axes.ravel()):\n",
    "    k.lengthscale = t\n",
    "    k.plot(ax=ax)\n",
    "    ax.set_ylim([0, 1])\n",
    "    ax.set_xlim([-4, 4])\n",
    "    ax.legend([t])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Task\n",
    "Try to change parameters to obtain more accurate model (we fix noise variance to some more correct value)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "######## Your code here ########\n",
    "kernel = GPy.kern.RBF(1, lengthscale=0.1)\n",
    "model = GPy.models.GPRegression(X, Y, kernel)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Name : GP regression\n",
      "Objective : 8.96143903620404\n",
      "Number of Parameters : 3\n",
      "Number of Optimization Parameters : 2\n",
      "Updates : True\n",
      "Parameters:\n",
      "  \u001b[1mGP_regression.         \u001b[0;0m  |  value  |  constraints  |  priors\n",
      "  \u001b[1mrbf.variance           \u001b[0;0m  |    1.0  |      +ve      |        \n",
      "  \u001b[1mrbf.lengthscale        \u001b[0;0m  |    0.1  |      +ve      |        \n",
      "  \u001b[1mGaussian_noise.variance\u001b[0;0m  |   0.01  |   +ve fixed   |        \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f1c27637ac8>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " /home/yeahrmek/miniconda3/lib/python3.6/site-packages/matplotlib/figure.py:2267: UserWarning:This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.Gaussian_noise.variance.fix(0.01)\n",
    "print(model)\n",
    "model.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Tuning parameters of the covariance function\n",
    "\n",
    "The parameters are tuned by maximizing likelihood. To do it just use `optimize()` method of the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Name : GP regression\n",
      "Objective : 6.244182033072176\n",
      "Number of Parameters : 3\n",
      "Number of Optimization Parameters : 3\n",
      "Updates : True\n",
      "Parameters:\n",
      "  \u001b[1mGP_regression.         \u001b[0;0m  |                   value  |  constraints  |  priors\n",
      "  \u001b[1mrbf.variance           \u001b[0;0m  |      0.9157310204033875  |      +ve      |        \n",
      "  \u001b[1mrbf.lengthscale        \u001b[0;0m  |      0.1396563412050284  |      +ve      |        \n",
      "  \u001b[1mGaussian_noise.variance\u001b[0;0m  |  2.5093239609568255e-09  |      +ve      |        \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f1c274118d0>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " /home/yeahrmek/miniconda3/lib/python3.6/site-packages/matplotlib/figure.py:2267: UserWarning:This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = GPy.models.GPRegression(X, Y, kernel)\n",
    "model.optimize()\n",
    "print(model)\n",
    "model.plot(figsize=(5, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Noise variance\n",
    "\n",
    "Noise variance acts like a regularization in GP models. Larger values of noise variance lead to more smooth model.  \n",
    "Let's check it: try to change noise variance to some large value, to some small value and see the results.\n",
    "\n",
    "Noise variance accessed like this: `model.Gaussian_noise.variance = 1`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f1c27372898>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " /home/yeahrmek/miniconda3/lib/python3.6/site-packages/matplotlib/figure.py:2267: UserWarning:This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.\n"
     ]
    },
    {
     "data": {
      "image/png": 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lSwiHw6xatarjvW3btpGWlsazzz6LqqrU19ezbt06FixYcELHFgIMBolFixfzbNsC384dO9i+fRsACxeezkcfbeDAgQMA+P3+4xq5n3/++Tz22J86Xjc1NfXrOP0haQRYkiRsNhul1c2JvhQdnRhkRaWhJRxTbNHQEuRXf9+ALygz/6Q8flS8sNeUsr4gSRJLL5zON78UXWh67OWtvPdZWZdxNquFhtYwwVDfDMptFgOhUDhuXzZL77IhSRIvvfQSb7/9NpMmTWL69Oncc889XHfddcyaNYvZs2ezZMkSHnjgAfLyuoZaeqK9KEUCvve9m/H5fMyaOYP777+PuXPnApCdnc2f//JXvnH9UubNPZWzFy9i7969vR73np/+jOamJk6dM5v58+by/nvv9es4/SEhdpQzZs0Rb77bfYO9YDhCqs2kL8rpJA2Hq5qQTGaMhqjwhCIKP3t8HYerWzhlfCb/79tnYRmg+B7LS+v28Y9/78RokLj3W2cya3JOzHYhBIFAkGljM7ukcZ6oHeVwQAhBOJKcJccJt6OUJOlvkiTVSZK0Y6DHslstNPoi+IN9u7vr6Awm3kCYiEqH+AoheOzlrRyubmFMppP/Wrow7uILcNXZU7ny7CmomuCBZzZSUeeN2S5JEmaLhYpRksapDFe3neMQrxDE/wEXxelYuJ02jtR69Tp4nYRT1eDDYT+6QPTWxlLWbS3HZjHyk6Wn43bEr8DhWJZ+cToLThlDICTzmyc/otUfWwBhMZvwh1W8/t4LI4Y7w9Xrty/ERYCFEOsATzyO1U77aq+OTqJobAkgGY/ObqsavDzxxnYAvn/VqRTlpvS6vxACfzCM3x8kEg6jyhFUOUIkHH3PHwz32nfNYJC4/avzmZifRo3HzwNPf9LFIc3psFFe7+syWUlEaHGwSGa3s+jPuf/XNmSLcJIk3SRJ0mZJkjY3eRqPO95kNKAIhk31j87IQtMEdU0B7G1GO6omeOT5LURklXNOLWLx7KIe9xVC4PMHUeUIRVkOThqXyaSCdMaPSWP8mDQmFaRz0rhMirIcqHIErz/UY/aPzWLinutPJyPFxq7SRp55a1eXMXa7Naai1Gaz0djYOCJEWEviJptCCJqaPBjN/S+MGbI8YCHEKmAVRBfh+rKP3WalvjlIitM2KHE2HZ2eqPP4sHRyOXtt/QH2lnlId9u44dJZPe4XjsgIVWFCXgo2a+857U67lQl2K2FZoby2FYGhW0/hzFQ7dxUv4N4/f8DLH+znlAlZzD/paPaAyWggEIFmb4g0t43CwkIqKiqor6/vx3eeXMiKmsReMRJGswVnWs7xh/ZAUhRi9IbTaeNITTOTCzOS+BehM5JQVY0mXwSXK1rxVlHnpWRNdOb5/avm4OqhFNgfCJHmMJOXlXlC57OaTUwuzKC+yU99a7BLpR3AyeMyue4LJ/PUf3bxyPOfsvzWJWR1MvBx2C1UNfpwOSyYzWYmTJjQ5RjDjfomP81BZUQXZyVNHnBPSJKEwWSmtjF5E891RhbVjd6OmaimCf744hYiisZ5c8cy/6Qx3e7j9QfJS3eQl+Xu93mz052My3Hj9QW6DUlcuXgqp07NxRuI8NDqjV3ivna7jbIRsm4iKyr1LaERLb4QvzS0EuAjYJokSRWSJN0Qj+O2YzGb8PgjfU4819HpL4qq4Q0oUbc+4P2tZewt85DmtvLtS2Z2u4/XF6Qo29XvKrjOOO0WJhek4w8Gu4iwwSBx2zXzyEixseeIhxfej63Miq6bSHhagwx3ympbcfQzw0TTBFUNPj7bV8v7n5WxZlMp731Wxqbd1RypaSUiq3G+2v4TlxCEEKI4HsfpDZfDxpHa1m4Tz3V04kVVgxdbW9pZMCzzj//sBOD6C2d0G3rw+qPiG890NIvZyNTCDPZVeHDa7TEZAKkuK7ddM4/7/raef767h3nTcpnUyRfCbrNQ4wngdlgwm4bnuomnNYgqwGLo+/yw2Rfmo+2VbN5bw54jjQTDPfs8mIwS4/JSmTctj4XT8xmfl7gu1EkfA26nPfG8qsFLQXbv6T86Ov1BUTV8QQW3K/rY+8+1e2n2hplSlM45c7pmPQSCYcakO3A7458LbDIamFKQzv6KZlxOW4xAzJqcwyVnTOL1jw6y8rlP+f0t58WUQTsc0RTOyYUZcb+uwSYiq9EbiKvnTiOdOVDRxEvr9rFxVzVqpyeGjBQb+Vku0l3RBXxZ1Wj1h6n1+Knx+DlY2czBymaee3cPuRlOzps7lgsXTCDVNXh53d0xbAQYoqGIVn+Q9GAk6T1RdYYfVQ1e7G2z36oGH6+tjxqx3HjprC55qOGITIrdRHpK34SiP5hNRibmp3CoqrWLIC29aDpbD9RSUe/l6bd28p1LjmZmGA0GZMlAfZOf7HTnoF1fvBFCcKSmGafj+KGcijovT/57B5v31ABgkGDetFzOmFHAnCk5ZPTyewmEZPYcaeSTXdVs3FVNrcfP6rd38+J7ezl7ThFXnj2F/AHE8k+EpPOCOB5CCIKBEFPH6lkROvFDUTX2lzd1ZD785smP2LynhvPmjuXWa+Z1GavKkSGbYfqCYcrq/LidscK0v6KJex57H00T3H/DWcyc1DkdSuD1hZhUkIrVPDzmWRV1LYRVCUsv16uoGi+8t5fn1+5F1QQ2i5GLFk7kkjMn9djWqTdUTbDjUD2vrT/Ap3trgWis/YL54/jqkpPJSOlfXL+vXhDDToABIrKC3SwN2V1KZ+RTUdeCrEmYTCZ2HKrn//3lQ2wWE3+86wukH7O45vUGmDY2Y0hN0Rua/Xh8MvZj8oSffWc3z76zB4tB4a8/vwKnzQIIli9/CJfLyfVLvzksJivNvhC1TcGYsu9jOVLTyiPPf8qhqqhj4hdOG0/xBSfHZfEToLLey8sf7Gftp0fQBFjNRq5YPIWrzpl6wk53Q2rGM9RYzCaa/bKeFaETF1RV4+FHH2flypUIofF0W7VZtrGOf5b8PWasLxCiKNc95B0pstKc2MwSETl2cenL507FZQwR0Uzc+bvVtItvSUkJPp8fo9lEVYO3+4MmCaGw3MVz41jWbDrM3X9cy6GqZrLTHNx/wyK+f9WpcRNfgIJsNz+8ei4PLzufBaeMISyrPPfuHu5Y+Q5b99fG7TydGR7PJt3gclgpq/MytSj57+46yU2tx0ckHObZZ0vwROzs9Y7BJKlseO2vjP3ql2lvJxSRFdw246Aa8PRGUU4K+8o8mIzGjpi0yWjkN7dewu0Pr6E+7GbxxUsJ1u2luLi4o+1RayCE2xciJQlbfimqxuHqVlzdFJ+0b//ba9v49ydRc/oL5o/j25fMxH6cKsOBUJiTwk+Wns7Oww2s+tdWyuu8/OKJDSyaVcgNl86K60LdsAxBtBORFZxmaUDJ7zqjG00T7C334HLaePDBh3iv1IElJY+mvWu49MxJMb3bfP4gJyX4cT4iqxyobO6yKPf6hgP89bXtqBE/1RtWsXHD+3R2UPD6AkwtysCURL3kNE2wv9yD1W7tsPvsTKs/zO+f2cjOww2YjAZuvnIOS+aNG9JrVFSNV9cf4Ll39hCWVVKcFm6+Yg6nzyjodb8RHYJop71AIxSWE30pOsOUhhY/FosZkDjzwq9hSclDCXnxlW+JEV9/IERhtivhT1sWs5ExGQ4CMX7Zgt0b/kWo8TBGi5OMUy7mwQcfIjpzj+JwRLvNJItBjxCCQ1VNWKyWbsW3vjnAzx5fx87DDaS5rfzyu4uHXHwhmg541dlTWXn7+cyYmEWrP8IDz2xkxepNeAMDtwEd1gIM0QKNstrWpPlg6QwfhBB4WsNYzCZUVeWPz64HoPXQBwhNibaOR6CoGnZL4kIPx5KeYsdullAUlfaY7+rVJSyaZMBhNeHImcar63Z2XD9EU9Mko4nK+sQbuAshOFjZhMFk7qg47ExFnZefPr6OygYf4/JS+P0PzmPa2MTmNOekO7nvO4v47mWzsZqNfLCtgmUr32HT7uoBHXfYC7AkSRjNZuo8um2lzonR5A1hMBkBwU9/9xeCmgWbQebtFx6juLiYkpISli9/iEAgREF2coW5CnNSCIUjgITb7aK4uJif/ngZN1w2G4CcmZdgsqfQOQxhMZvwhbWElipr2lHxNbf97DtzoMLDz1ato7ElyLSxGfzyu4v7lV42GBgMEl86YyIrblvCKeMzafaG+Z9/fMwfX9xCsJ9P4cN2Ea4zFrOJRm+QVLd1xJt36MSPhpYgdrst6h0Qjs6wbrhyASajsS38AHaHk+w0W1LFTiEqBmNz3JTVebnppu/RvlB47qlFfLKrio27qmm0nISmiZgiEqfdSk1TAIvZgKuXrIPBQFU1DlY2YbZYMJmMrFr1OF6vryPUs7/cw08fexdVGJk7NZe7r1uA1ZJ8EpWX6eIXNy7m9Q0Heeqtnbyz+Qg7DtZz21fmcfL4rBM6VnJ9qgaAy2mjvDbxj1c6wwNvIIxo+/h/sqsKv2wiK83O2XPGto2QuOuuO/nWN75JTnpyNoh12i2kOi1tqWlRkZUkiZuvPJUUp4Udhxp4/aODXfZzO+2U1foIRYZu7SQiq+yr8GC2WtvCDgKv19fxlBEV37WowkimxcdPrl+YlOLbjsEgcdmiyfz+h+cxIT+V2qYAP//zBzz57x3ISt/NfkaMAEuShGQ06baVOn2itimA3WZGCMHz70XbjV+1eCpm09E/CX8wwpjM5C7lHZPpQpXlmDWQNJeVH1x1KgD/+PfOjsKFzricNg5VtpyQWPQXXzDMgcomHHZ7pyeJ6A2uuLiYF954n7v/8B9UYSDT4uNP916HyTg8jITG5qbw25vP5ZpzpyEBL6/bz4//970+7z9iBBjAajHT6A0P6Z1dZ/gRjihEFA1Jktiyr5bDVS2kua0smX90lV0IgclAUubOdkaSJMbmpuALhGLeX3BKPhcunICiaiwv2dglRilJEk6nnf0VzYNqz1jf5Ke8zo/b5eimr5vEZV/9FjlzizGYbfhrdg0r8W3HbDJw3RdP4dffO5sxmU6O1PT9SXxECTBE7+xlNXpWhE7P1DT6cNpt0dnv2ujs9/JFU2LKTf2BEIVZyRl6OBab1UyG00L4mInHty6eybi8FKob/fz5lc+77GcwSLicNvZXNMU9lVNVNUqrmmj2y7ic3d/E9pU38rPH3usQ38bt/2Llww9z7MLccGHa2EwevGUJFy7oezeSESfA7VkReihCpzsUVSMQiXbZ3Xm4gb1lHlx2c8wfjapp2MyG4/Z0SyZyM11oihIz8bCajdx17WlYzUbe+6yctVvKuuwnSRJul51D1S00+0JdtveHVl+IveVNCKO52x53AHvLouLbHnZ4488/ofjar3XEhIerCNutJr535Zw+jx9xAgztBRq6V4ROV+qa/Njamm2+8mHUbvKSMydhtx5d8AkEw8POc1qSJMaNScXnjxXRwpwUbrwsalX5+L+2crCyazw4KsIOapuClNW29Nih+XjIisrhqiaqmoK4XfYeM0f2HGnkF09sQBUGsiw+Hrv3OoxtmSfFxcW43S6Ssw9y/BmRAgxRr4jS2tZ+f5h0Rh5CCFr8EUwmI5X1XjbvqcFsMnDRwokdY1RNw2k1Dcsu3FaziaxUa5c1kCXzxnH+vHFEZJXfPvUxzd7uZ7oOuxVFGNhb7sHTGuxzGC8iq5TVtLC/ohnJZMbZS3rb7jbxDYYVFs0q5E9t4hslujAXTasbHYxYAZYkCavVSkUSVP7oJAee1iDmNq/Z1zZE07POmVMUY64SCITJHyax3+7ISXeBqsRMPCRJ4qYrZjNtbAaNLUF+9/QnPWY/mE1GXE47jb4Ie8s9VNS14A+GY44nhCAcUaj1+DhQ4eFAVQuawYjbZe+2rLid3aUN/PKJDYQiCotnFbLsK/M6iW/H1Q7o+x9ujFgBhuiHKRDRerzj64wuGluCWC1mvIFwRzz00rMmd2xXVA2XzTRse6m1My4vDX8gttrNbDLyX19fSGaqnb1lHh57eWuvM1ybxYzTYUfFREVDgD1lHnaXNrLnSCO7j3g4XOPFHxFYbTbcTluvwguwdX8tv/y/NvGdXchtX5k35JaeyUjyZjrHCafdSlWjH4fNnHSPlZomaPaFaPU95mgrAAAgAElEQVSHkRUNTRMIwCBJmEwGHBYjmWmOYS8IyYA3EEZI0Z/jWxtLicgqc6bkMDb3aKw3FAozuSAtUZcYNyxmIzlpdjy+MHbb0dl9mtvGPdefzk8fX8faLWWku20svXB6r8cyGKRefXr7wrqt5Tzy/KeomuCcU4u45cvzMHZJSRudjIpbkNNh43BV8jhByUo0Zra3zIPHF8FotmCz23A47TidduwOG2aLhaAC+ytbOFDZdIz7lc6J0l54ISsab3x0CIDLFx2d/bbHfkfKzS4rzYlJis7qOzMxP40fFS/AaJB48f19HWl4g8Wr6w/w8HObUTXB5Ysmc2sfxFcIgT8Yxh8IIkciaHIEVY4QDoXx+YKEIz13PB5ujPgZMETv4marmfK6VsbmpibsOoQQVDf6aPFHsNutuFy9pzmZTEbcJmO0WWG9D6fFSEH20HdjGO6EZYWIrGG1SmzYXk6TN0RRjpvZk4/2UAsEw0wZAbPfzozLS2VvuQe3yxHz/vyT8rj1mnms/OdmnlmzC1lRufaCk+NqtRmRVf786ue8s/kIAN/40gyuXDzluPv5AyEsRomxWc5uG+9qmsDTGqShJYjZYu61f9xwYHhf/QlgNpkIhiIJ6xQbDEUoq/Vitpp7dP/vCUmScDlsKKrG3vImxue69a7QJ0Btox+Hw4oQglfXRxffLls0uUNwNE3gtBhHzOy3HaPRQGGWiypPoEun4bPnFCGAR/65mX+u3YvHG+J7V8yJi+lQrcfP75/ZyKGqZiwmA9+/ei7nzCnqdR9FUQmFIxTluHo1CTIYJLLSHGSm2qlt9OHxB3E5bAn3ae4vo0aAAew2C/WtIWwWE27n0DlB1TX5aGgN4z5B4T0Wk9GA22WntM7LmHTHoLZEHymoqoY/pOBymdl5qIFDVc2kOC2cPfuoIPgD0e7BI5EUl43WQJiwrHSZLZ4zpwir2cjDz23mnc1HqKr3ccfX5pOV5ujhaL0jhGD99kpW/WsrvqBMboaTH1+3gAn5vT9ZhCIyZjSmFWV0U67cPZIU7YST6opwuMaLw9F9V41kZ/hd8QBxO22U1fuGpIuGpglKq5po8Sv9EN9j49VHX7uddupaQtR69Gq/49HQHMDSVtH26vpo4cVFCyd2LMgKIbCZDcOmdXt/KMhOQVPkbnPiT5+ezy+/u5iMFBu7jzRy5yPvsmbT4RPOn6+oa+U3T37EQ6s34QvKzD8pj9//8Nzjiq8/GMZtMTA+P73P4tsZu83C1KJ0IqFwm0H98GLUCTBERfhQVcugmpDIisr+cg+awdRjOWZPrFr1+DHlmNGuB6tWPd4xxmG30uxXdBE+Dk2+aMeL6kYfm/ZUYzIauGjh0bLjQDCc9I5nA0WSJMaPScMf6D4dc0phOstvWcK8abn4gjJ/emkrP/rjWj78vKItX7j7yYAQgr1lHlY8u4nb//Aun+6txWE18f2r5nDP9afjOk6YzBcIkeW2DLino8loYHJhBoosDzsRjsttX5Kki4CVgBH4ixDit/E47mDR7gR1oLKJKYXpcY/9+YMRSmuinV5P/K5+1CcV4K677uxoM15cXEy78TaAw26hyR/GaPCTlTayRaQ/tHhDGNoS/V9bfxAh4Ow5hTGtzI2G6CxqpGM2GSnKdlHR4Ot2DSLVZeWn3ziD9dsq+b83t1Na3cJDz27CJGmkmgN86bwFpLlsGAzwyutrkA0OwqYMGpqj+cYGg8SFCybw1fNPIr0PreJ9/iB5cQyjGQwSkwrSOVDhAcmadAb6PTHgrsiSJBmBfcAXgApgE1AshNjV0z7x6oo8UDRN4A+EmFyQFrcc4abWINWeQJeutb2hqhoNLUFa/eHozcFu4uknVrF6dUnHmM5txo/F5w+Sn+kkNcmtE4ea/RUebDYbvmCE7/7234RllRW3LWFcXjTeGwxFyEu3kdKDW9dIpNbjozWg9PpUFpFV1m4p4z8bD1Fa3XslaUaKjcWzC7n4jElk9zF27AuEGJPuiLkRxgtV1dhf4cFu78/kJ370tStyPGbAC4ADQohDAJIkrQauAHoU4GSh3Y7vQGUTY3PdA2rRIoSgsr4VX1jrk/g2tARZv62CTburOVDZ1ZPVYppMzvylBOv24q/e0aP4AricdiobfFgtRr0lUxvBUASlLQV2zaZSwrLKrMnZHeILgNBGlfgC5Ga4CEdaiHSzKNeOxWzkwoUTuHDhBKoavDz8+DNs2XUYg9mOJBmYPKGIS7+wmMlFGUzKTzshofP6Q+RnDI74QjTzY2J+Ovsrmkhx928xcSiJhwAXAOWdXlcAC+Nw3CGh3QmqvM5PZorcr/YzEVnlSE0zhuMYkQAcrm7hhbV7+XhXVcxCR0aKrePRrcUXpqEliC1jHLaMcaROOZcf/uLv/O7u4h5vEi5n1FJwWmGGnicM1Hj8OGxWFFXj9Tbfh8s7lR2HIjJZSdLscagpyk3hYGUTiiR125W4M/lZbh742U3Mn39ax3v/eWIT/fFsGGzxbcdiNjIuz01ZnR93kt9gh2zpV5Kkm4CbAPILCofqtH3G5bTRHIjQ6vdQlJvSp1VxIQR1Hj8ebxiHw9brTKDZF+bvb2zn/a3Re5XRIHHGjHzOmlnIjIlZpHSkxUUX3D579yXOv3wpzvyZfLavjuqQhRt+9Sq3fe10zprV9ecnSRJ2m40jNS1MLEjv189gpKCoGiFZw2WRWP95BZ7WEAXZLuZMyT06RlZIdw8vy8l4IUkSE/P7Gi8VbQvCR1m+/KFen8i6w9sWJksbojCZy24lK0WmJRDpsB9NRuIhwJVA5yzrwrb3YhBCrAJWQTQGHIfzxh271RJtm13Vit0skZPu6HZGq6gantYAntYwZosZVy8hByEE67dV8pdXP6c1EImuwp8+gSsWTemh3Xa0zfi1X7mKu+76HiBxuKqJ+x97k1bFzvLVm9h2sJ4bL5vVZfHQZDQQUiTqmnxJ20hyKGj3/BVCdHj+XnbW5I4bZERWSHdahm3yfjw4umjVBLaeRFjELAB3XhAG+izCXl+QomzXkObeQ9QZzhdoQlG1pF2Ui4cAbwKmSJI0gajwXgtcF4fjJgSDQcLtjLarKW8IgObDbDJ0/LGqqoasCSxmM87j5Pb6ghEefWELG3dVAzBzYjbfv/pU8jJ6z1jo3GYcYEJ+Ok/cfy3/+aSUJ97YzppNpVQ1+PivpQu7pPrYrBYaWoOkOKzDqqNDvGj3/HU57ewubeBgZTNuh4VzTh3bMSYSlhmfM7qfEiAaL51cmM7ByiaExdJNNlB0MtB5ATj6L30yTY8ucgcZl5uCM0GVm9Fy7KYTWhQfSgacBQEgSdLFwMNE09D+JoT4dW/jkyULYjCpafTx679/RGWDD7vVxLcunsEF88cPeNZ1qKqZ3zz5EZ7WEGNzU7j/hkUxfrYQFaFgMMTUooxRN8trbAnQ5JexWsw88PQnfLyzimvOm8Z1X4guSKuahkFTGZs3Mivf+oOmCUqrm9EkA9ZuF3GPTga6f90VWVGJhMNMzE9PuAuhLximvK779LvBoq9ZEHGZlwsh3hBCTBVCTDqe+I4Gdh9p5Cd/ep/KBh/j8lJYcdsSvnDahLiI4cT8NH578zkUZLsoq23lvr99iDcQjhkjSRJmi5nKUWhG3+75W+Px88muKkxGKabjRSAYIS9z9IZnusNgkJhYkI7LYuihWKNrN+PeCIYiGITK1KLMhIsvROPBKQ4zETn5XNSSMzAyjFm3tZz//suHtAYinDo1l1/fdDY5cTb/yUpz8IsbF1OQ7eJITSu/efLjLhZ9ZpMJb1DBP4psLFv9IYQU/Ui/viFaeLF4dhEZKdGFHyEENpOUFKKQjORluSnIcuLzB5GVExcrRVHx+YNkp1gZP+bE0tMGm/wsN4osJ40lbTu6AMcJIQTPvbOHh5/bjKJqXLRwAj+9/nQctsGJw6a7bdx/wyKy0qIdDlY8t7lL/b7Laaeizpt0H7rBoq45iMNuxR+SO2wQO3e8CIQi5GYkf25oInE7rJw0NgOHScLn75v3bkRW8PmDmA0aUwvTk9IkSpIkxua48R3ztJhodAEeEFFhkxWVP/zzU1a/sxuDBDdcOovvXj570PNxM1Ls/L9vnYnTZmbjrmpeXLevyxiTxUx148j3iwhHFCJtlRdvbyolFFGYMTGLCWOOxnoNiOPmaescdRqbVpRButNEOBTC5wviD4QIhMIEQmH8gTA+f5BQMITLYmBqYTqFOalJnYNut1lIcyZXKGLkWkANMqtWPY7X6+O7N/+Q3z21kd1HGjGgMSe7lUvOnNTv47bPYvv6+FaYk8Kyr87nN09+xOo1u5hSmB5jNG4xm2j2B8lIkUd0lVxNow+n3Yaqarz+UVvhxSK98GIgGAwSmakOMlMdCCGIKCqKoiFJYDQYsJiNw26Rd0ymi31lnqQxck/e21VSEzXM+ee//sPN//MKu480YjEoVH70N+yqh67uUd2jaYJAMILfHyQSDqMpMkYUjChonVqwHO+OPf+kPL5y3jQ0AStWb6KhJbYho8tho7x25C7IKapGIKJiMEh8vLOKhuYg+Vku5k7N6xijykqfTGJ0ukeSJKxmE067BYfNgtViGnbiC9HvoyDHha8HZ7ihJjluA8MOiQuvup5PPOMIaUYirdVUfvYcX736sj4lp4cjCnJExmkzUZhl7/WxWNMETd4gja0hMBiw91DV89XzT2Z/RRNb99fx4DOf8Kubzu5IPpckCWEw0tgSIDN15MVAaxq92NqaT7Z7/l565qSOpwhZUUkZ5YUXOkdx2a04LSEURT1uKfZgo8+A+8G7nx7hF09sQBFGAnX7qN30D9Sw77jiK7etErutBqaNzWBsXupxY5Ltj4FTizLIdFnw+YOomtZlnNEgcftX55OVamdfeRMvvh8bD7ZbLdQ1B1HVrvsOZzRN4A0omIwG9pY1sq+8CZfdzLlzjxZehEMRchPQhkoneSnIdhMMJX5BLiEC3OqPtBk9Dy80TfD0Wzt59IUtKKog39ZMw9bnEWq0u0asifpRhBB4/UGsRsG0ogxyM139StHJTHUwpTAdJRLpNiyR4rRyy5fnAvDPd/dwuKo5ZrvNZqWy3nvC501m6pv8RztefBiN/X5xwQRslujDnaYJHFZjUi8O6Qw9RqOBMRnOhItwQj6Vja0hfvjQGtZuKUM9wdYniSIUUXho9SZeeG9ftI7eWc/Hr/yR4uJr2bx5E8XFxZSUlHQR4XBEJhwKMSk/lYLslAHnRra7/1uNglC4a47vrMk5fOn0iaia4A/PfxpzozMZDfjDCsHQyMgNFkLgaet4Uevx8/HOSowGiS+d3qnwIhTWCy90uiU9xY4BccLtl+JJQgTYYjLQ0Bzkkec/5a5H3mXznpqkzlWta/Lz08fXsWFHJQ6riZ9/8wymZIsuNfLFxcUxNfJefwi31ciUosy49xwrzEklxWbqVkyvv2g6eRlOjtS08ty7e2K2OR02yutGxizY0xrE3PZzfXX9ATQBi2cXxpgcmQxgtehLHTrdU5Sbgj+YuAW5uHhBnCgzZs0RP35wNSVv7+poaXLK+Eyuv2g608ZmDvn19MaOQ/U8+MxGWgMR8rNc/GTp6RTmtPew6r5GXtU0AoHQgE3e+0Jto4/WkNLFcm/3kUZ+vmodEvC7H5zLpE4WlcFwhAynedi3MdpT1ojTYccbCHPT7/7TTceLMLlpdr1TiE6vVDV4CcoirqlpQ+oF0R/OmzuWR+/4At++eCZuh4VdpY3c89g6fvvUx1TUJT5lSlU1Vr+9m/v+erSs+HffP6eT+EJ3NfKKohIOhplalDHo4guQm+nCbpYIR2K7PJ88LpNLz5yEJuCxl7fGhHrsVgv1LaFhvSDX1Brs6Pf2748PE5ZV5kzJiel4oWmaLr46x2VMpovIEHRJ746ErkxYzEYuWzSZ//3RF7nm3GlYzUY27qrm9pXv8McXt3TJZx0q6pr8/PzPH/Dcu3sQwNXnTOWn3zjjuJZ6sqKgKjJTijKG1H+0MCcVo9C6dIS99oJTyEq1c7CymX9/fChmm81qobJh+IYi6psD2K0WIrLKGx9Fv7crF0/p2B6OKKS79Ko3neMjSRL5WU4CCfBNSYqlYafNzHVfPIU/3vVFLlwYdQ17Z/MRbln+Fk+8sZ3GIRJiVdV4df0B7vjDu+wt85CRYuO/v30WSy+cjvE4i2cRWUFSVSYVpCfEhGTcmDTC4UjMgoLdauLGy2YB8MyaXTE/R5PJiC+kEkrQnX8gtHijOdEA728to8UfZkJ+KjMnZXeMkSMy2cM8xKIzdKS6bJgMQ78glxQC3E5Gio3vXTGHlbdfwJkzC4goGq9+eIDvP/gfHn3h00ENTew81MBdj67lide3EwwrLDxlDA/duoRZncp6e0JWVCRNZXx+WsKS/Q0GiYn5aV3sBBecks+CU8YQDCv89bVtMdtcDivlSRDuOVFqmvzYbVY0TfDKB9HCiysXTzlqmq9pOO2mpHLj0kl+inJSerDjHDyScnk4P8vFj4oXcPDsZl56fx8f76zk3U/LePfTMk4Zn8kFp43njBkFWAdoKyiEYMu+Wv61bj87DjcAkJvh5IZLZzL/pDF9OoaiamiKzKSC9IRXWlnMRvIzndQ0B2MKPG68dBbbDtTz8c4qPt1bw7xp0RJdSZIQkoGm1mBSOlh1R4s3hNQ2+928p5rKBh9ZaXbOmFHQMSYQjDA5Xzdc1zkxLGYjaS4LIUXBbBoaaUxKAW5nUkEaP7puAdWNPv71wX7WbS1nV2kju0ob+csrn3Pq1FxOO3kMc6fldmnN0xt1TX4+2lHFu58e6UjJclhNXL5oCleePaXPfrFCCEKhEFMLk6fzRJrbRmsgjKyoHS1mstIcXHvBSfzfGzv4y6vbmDkxu+N7tNus1Hj8pLp6byqaLNR4/DjaOhu8/MF+INrvrT3mrnv+6gyEMZku9pR5dAHuzJhMFzdfeSrfuGgGH26rYM2mUg5WNrN+eyXrt1ciSdFZ84QxaYwfk0qay4rTbsZhNaNqAn8wQn1zgCO1rewr81Dd6O84dkaKjUvPmswXThuP8wS9e33+EJMK0pKuyqowO4V95R7MpqOz2ovPmMS7n5ZRVtvKyx/s56tLTurYZrVZqWpopTAnuWeNntYgUtvPem9ZI3uOeHDazFwwf3zHmEAoQlHWyPO70BkaJEmKPkU2hXAMQR+7hOUBD7QnXI3Hz+bd1WzaXcOu0oYTqqhzWE3MnpLDolmFzD9pDGbTiQtoIBjNMU1LUoctfzBCWZ03pg/WzsMN3PvnD7CYDKy8/QJyOzUH9fqDTByTkrSWlUIIfnTv71BVmbvuupPfPvUJG3dVU2hvYkau3NbIFELBEFOKMhJ8tTrDnYOVTZjMln4/FfY1D3hYzIC7Iy/DyaVnTebSsyYTkVXK61o5VNVCWW0rvmCEQEjGH5QxGQ3YrSay0hwUZLmYVJDGxPyBzVplRcFpNSSt+AI47RbcdhNhWelIMJ8+IYtz5hTx/tZy/vb6Nu65/oyO8S6HlfLaVqYUJVchTDv1TX7CcoR/Prsav2Jha0shBjQ+fvPvjPvy5YAgFFFiquB0dPpLUU4KByqbB72b8rAV4M5YzEYmFaTHVHsNFkIIImGZCWOTf5ZVkJ3C3mPMp7/xpRms//wIm3bXsHlPddtio+Chh1Zgszv58e3fJyPJFuQ0TdDoDfNfd9+FySDx1s5WnHnQcmQzX/vy5R3l4IqskO5OSfTl6owALGYjGS4L/k4TmMEguYKXwwBfIMT4vJSkWXTrDUmSKMxxxaTWpLutFNk9ACx/6gPCssLy5Q9RUlJCKOinxuNPugq56kYvVqsFkPjq0htx5J6M0BRaSz/uEN+IrJCue/7qxJHcTBdyZHDz5HUBPgEiskKG04LNmpxx0u5w2a04LEaUDlGVeOCe7+AwhglrZr709bspKSnpMBay221UJJFlZURWaQ3IbRkdgl/+6V9IkoSv8nPUsLfDfS4SlsnWPX914ogkSRRkuwY1N1gX4D4ihECRZXKHobVhQbabUCffU6PRyE+/cz4AqRPOxGhP65hJmowGghEVrz/xZtUAFXWtOOw2QPCrBx6hPuxEQvD0H+7psAD9/YMP4bTpnr868cftsGIzGzpNYOKL/ontI/5AiKJs97B8xDUaDeSmOwh1WFcK3nzxSfxV25CMJjJO+mKMj7HTYaOi3pdQn1SAVl+IiNbeoFSiRs5CkgycP388OenODgtQi9XGmCz3cY+no9MfinJSCAYHZ0KiC3AfUBQVp800JHmBg0VGih2EihBaR8z33OmpOKwm7NlTePntzTEibLVZqKhPXJmypgkqG/0dFX3lta3UBOwYDRJXnzutbZTEHXfcwQ+/d2NH0YmOTryJTmDsnSYw8UMX4D4QCkcoGAEzrKKcFHyBCG63i+LiYu65exnFX4imKhbOuwqH86iZvNlkJBBWafUlxqy6qqEVS6ec5Kff2oUm4ILTxpPXKX85EIowZhiGhXSGF5mpDiS0uD8Vjog0tMEkGI6Qk2YfEfFFm9WM22bk29+5sa34ROKihRN4e3MpR2paSZ98dsx4p8NGZYMPp90ypN9/IBihNajidkbzrHcfaWTj7mqsZmNMBZ8QArNRGlaLojrDl7G5qXHPDR7QX5UkSV+RJGmnJEmaJEnz43VRyYIQAlR1RLVyL8hOIRwK0z7TNRoN3HT5bABeWreP6kZfzHi7w0ZpTcuQXZ+mCcrqvB3iK4TgqX/vBOCyRZNJ71T8EghFyMsYOb8bneTGYjaS6bZ2aX4wEAY6rdkBXA2si8O1JB3+YJjC7OEfeuiMwSCRm+GMiWedPD6L8+aORVY0/vrqtpj+fEaDARWJ2mOEebCoqG/F0qm90uY9New+0ojbYYkxXAcwIoak64iOTju5mS6EqsSth+WABFgIsVsIsTcuV5JkqJqGzSQN64W3nji6IHf0Q3T9hdNx2Mxs2VfLpt3VMePtVgseX3jQU9OaWoMEI6JjQU1VNZ76T3T2e81503B0MksKhiLkpuuzX52hpyg3BZ8/PmsjQxbYkyTpJkmSNkuStLnJ0zhUp+03gUCYwpyRW9ZamO2OSTBPc9u47gsnA/DnV7fhD8U+ZrmcdsrrfYQGqTIoFJap9gRibnhvfHSI8jovuekOLlo4IWa8JDRS9H5vOgnAZjHHLRRxXAGWJOltSZJ2dPN1xYmcSAixSggxXwgxPz0jOQ1f2pEVlTSXZUSnNtltFpxWU0yC+YULJjClMJ3GliD/98b2Lvu4nDYOV7XGPSldVlQOVbXgch4V1MaWICVv7wbghstmxfwugqEwOWn67FcncbSHIgaaFXFcARZCXCCEmNHN178GdOYkJhyOkJcx8lObulbIGbj1mrmYTQbe2XyELftqY8ZLkoTdYeVARVPcRFhVNQ5WNuN02mOKXJ54YzuhiMKCU8Z06U4iNI3UJHai0xkdjMvr2gLsRBn+uVVxJhSRyUoZHt0hBorRaCArxRYTVijMSaH4gmgo4n9f3IL/mE6xRoMBm93KgQoP8jFdmE8UVdXYX9GEzW6N+Xlv3V/Lhu2VWM1GvnPJrJh9gqEwebrng04SYDEbyctwEBxAgcZA09CukiSpAjgDeF2SpP8M5HjJgCYro8rUJTvdiVBiV3UvWzSFqUXpeFpD/O31rqEIo8GA3W5nf3lTvz98oYjMvvKo+BoNRz+GEVnlz698DsBXlpxEzjELbfrsVyeZyEixYzFGq2X7w0CzIF4SQhQKIaxCiFwhxIUDOV6iCQQjjMkcPeLbTmG2G3+nWnejQeLWa+ZhMRlYu6WM9z4r67KPwSDhdjs4XOs94RS1hmY/h6tacTptMeIL8PRbO6lu9FOY7eaysybHbAsEI4zJGH2/H53kZmxuKsFwuF+paXoIog0hBEaDGJUr6w67BWeMZWU0PnzDZdECjcde3sqRmu59IdxOO96wyt4jjbR4Q71+CL2BMPvLG2nyybhc9i7GRjsO1fPq+oMYDBK3fmVel1ZRBtRR+fvRSW4MBomJean9Sk3TBbgNfyBEYdbIX3jriYJsdxfHpwvmj+O8uWOJyCq/f+YTguHu026sFjMOp53alhB7yzyUVjdT2+ijodlPrcfHkZoW9pY1UtUYxGa3Y7N1za1u9oV5+LnNAFxz7jSmFMZ2NwkEw4wZxb8fneTGZjWTk2Y74ZCcLsBEiy4cFuOo9hQwGg3kpNliKuQkSeKmy2czLi+FqgYff3zhs15nuHabBafTjtFsISALWoIq/ojAYDLjcNh7LGpRNcHDz23C0xri5HGZXHPetJjtmiYwGdCr3nSSmqw0JzazhKwofd5HF2AgGAiTP8JKjvtDVpqzS4Wc1WLi7usWYLea2LCjsiM393iYTEYsZlOfcqn//uZ2th2oJ8Vp4c5rT8N0jPGPPximMEf//egkP0U5KSgRGST6lEY16gU4IiukjvCiixNhbDexrPwsN3deexoGg8Tza/fy5seH4na+1zcc5LX1BzEZJe4uXtilq7GiqLhsRqyD2BhRRydeSJLExIJ0hKr1KVFeF+BRUnTRV6xmExkuCxE59jFq3rQ8br5yDgB/fuVz/h0HEV6zqZS/vrYNgB9cPZfpE7O6jBkpXsw6oweT0YCmRoJ9GTuqBTgYjpCT7hgVRRcnQm6mC1WWu8R7L5g/nhsujRZGrHrlc559Z3e/Um+EELy2/gCPvfwZAN+6eAbnnjq2y7j2opiR4MWso9Mdo/aTPRK9fuOFJEmMzU3B102Z5SVnTuJ7V8zBIMGz7+zh989sxBvo+8pvKKLw2Mtb+dvr2xECvvmlGVy+aEqXcUIIhDK6imJ0Rh+jNrAWCIYp0hfeesRmNZPhtOCLyFgtsdkhFy6cQGaqnYdWb+LjnVXsLfOw9MLpnD2nCKNBItpXrvNThUAI2LKvlr+9to3qRj9mk4FbvzyPRaEGV7UAAAj4SURBVLMLuz2/LxBiYt7IdaPT0QGQ4mUsfCLMmDVHvPnuhiE/bzuqpoEiMz4//fiDRzn7yxuxWLv3xqjx+PnDPzez54gHgDGZTpxqLXathdt/eAMGyUBDS4A/PvECHiWF1khUyMflpXDbNfOYkJ/W7TkjsoLdLJGvx351himSJH0qhDhul6BRKcBeX5CpReld0p10uiIrKvsreu6DpWqCdVvLKHl7Nw3Nva87pDgtXHn2VC45Y2KPWSdCCELBEFOKMrpUyunoDBf6KsCjLgQRkRUy3VZdfPuI2WQkP8tJbVMQRzeFEEaDxHlzx3H27CI+P1jPxzsq+eizfbQGFZAMqCEv+ZkOvnH1ucw/aQw2S+8fOZ8/xMQxKbr46owKRp0AK7JMTl5Goi9jWJHmshEIyQS6iQe3YzQamDs1l7lTc/nB1acyf/5pHdte27wJ+pCXHgpHyEmzjeqKRJ3RxaiaBvoCIQqyXfrsqh/kZ7kxCK0PtnuC5csfinkn+rr3UFdEVrAapWg1no7OKGHUCLCiqDgtRt1PYACMH5NGJByh5yKfqPiWlJRQXFzM5s2bKC4upqSkpFcRVjUNVZYpytWzHnRGF6MmBBEKhZk2Nrl70SU7BoPEpMJ0DlR4sNm7evmChNvtori4mLvuuhOQ2v4Ft9tFd2EITRMEgyGmFuqLbjqjj1GRBeEPhhmTbidV95KNC4qq9SLC0F0ecE/i6w8GmVKQrntx6Iwo+poFMeJDEIqiYjNJuvjGEZPRwJTCDJRIpAfrvWPFtqv4KooaTTfTxVdnFDPiBTgYilCUo8cW443RaGBSQTpmSZxwZ9hgKIKkKUwpytDFV2dUM6JjwL5AiKJsl27mMkhIkkRRbipef5iqBh+SyYjd2r3pOkQzHaLuc07SU7ov7NDRGU2MWAGOyAqpDjNup571MNi4nVam/f/27i5ErrOO4/j3N/uW3XWTbPPSRJNtWmzEEAVLkHpjlRQpRZoLi1QoWgyWVPDGC1FyI3olohdiQXMhvuBLVVAXVLDVlkBxq4HWtBYNsdY2tdiaxjRkX2Zn9u/FOY3LMrNzZmc9z5zd3wcOnJnzzM5vDzN/zjznnOcZH+HS63NcfH2OeiOo1WrXeh6WmksMDYhtbxpm154dPtlmltuQBfiNy5r2+oaLUk1uHWVy6ygRQX2xSXNpiZrE8NCgh/w0a2FDFuDZ2XkOeiyBZCQx0uGWYzPbgCfhrlydY+r6CY/1YGZ9b0NVqatzC+yZHPPdbmZWCRumAM/NL7B9dJDrfHbdzCpiQxTg+foiY8M19ngAbzOrkMoX4PmFOlsGYN/ubamjmJl1pacCLOnLkv4i6aykn0lqPcfM/8nsXJ3xkQH2X+/ia2bV0+sR8MPA4Yh4J3AO+FzvkYq5cnWeHRNDnjfMzCqrpwIcEb+JiDdGY5kBWk9xu44azSWuXJllave4B+82s0pbzz7gjwO/brdR0v2Szkg6c+m1i2t6g6tzC9Bc5G1T1/lSMzOrvI63K0l6BNjTYtPJiPhF3uYk0AC+3+7vRMQp4BRk4wF3E3K+vkhzscHeHeMeVtLMNoyOBTgibl9tu6T7gA8CR2MdR3dfWgrm5uvUWGLn9jEmJzxTrpltLD3dsC/pDuAzwG0RMdvL32o0miw2mzQaTQZqMDo0yNSuccZG2w9vaGZWZb2OmPJ1YAR4OD86nYmIE51eNFCr0ajXAZCgJjE2NMDoxBbGtgx7HAcz2xR6KsAR8da1vG5osMaNby71kmEzs77jQ00zs0RcgM3MEnEBNjNLxAXYzCwRF2Azs0RcgM3MEtE63rxW/E2lV4F/lP7G3dkJ/Dt1iDVw7vJVNXtVc0P/Z78hInZ1apSkAFeBpDMRcSR1jm45d/mqmr2quaHa2ZdzF4SZWSIuwGZmibgAt3cqdYA1cu7yVTV7VXNDtbNf4z5gM7NEfARsZpaIC7CZWSKbugBLukPSXyWdl/TZFttHJD2Ub39C0oHyU7ZWIPunJT0r6ayk30q6IUXOlTrlXtbuQ5JCUl9calQkt6QP5/v8z5J+UHbGdgp8VqYkPSrpyfzzcmeKnCtJ+pakVyQ902a7JH0t/7/OSrql7Iw9i4hNuQADwN+Am4Bh4E/AoRVtPgl8I1+/B3gode4usr8fGMvXH+iH7EVy5+0mgNNkM20fqUJu4GbgSWAyf7w7de4usp8CHsjXDwHPp86dZ3kvcAvwTJvtd5JNBCzgVuCJ1Jm7XTbzEfC7gfMR8VxE1IEfAcdWtDkGfCdf/ylwVP0xMV3H7BHxaPxvmqgZYF/JGVspss8Bvgh8CZgvM9wqiuT+BPBgRFwCiIhXSs7YTpHsAWzN17cB/ywxX1sRcRp4bZUmx4DvRmYG2C5pbznp1sdmLsBvAV5c9vhC/lzLNhHRAC4DO0pJt7oi2Zc7TnakkFrH3PnPyP0R8csyg3VQZH8fBA5KelzSTD5fYj8okv3zwL2SLgC/Aj5VTrSedfs96Du9zglnfU7SvcAR4LbUWTqRVAO+CtyXOMpaDJJ1Q7yP7NfGaUnviIj/JE1VzEeAb0fEVyS9B/iepMMRsZQ62Ea3mY+AXwL2L3u8L3+uZRtJg2Q/zy6Wkm51RbIj6XbgJHBXRCyUlG01nXJPAIeBxyQ9T9avN90HJ+KK7O8LwHRELEbE34FzZAU5tSLZjwM/BoiI3wNbyAa76XeFvgf9bDMX4D8CN0u6UdIw2Um26RVtpoGP5et3A7+LvPc/sY7ZJb0L+CZZ8e2X/shVc0fE5YjYGREHIuIAWd/1XRFxJk3ca4p8Vn5OdvSLpJ1kXRLPlRmyjSLZXwCOAkh6O1kBfrXUlGszDXw0vxriVuByRLycOlRXUp8FTLmQnUU9R3aW+GT+3BfIvvSQfRB/ApwH/gDclDpzF9kfAf4FPJUv06kzF8m9ou1j9MFVEAX3t8i6T54FngbuSZ25i+yHgMfJrpB4CvhA6sx5rh8CLwOLZL8wjgMngBPL9vmD+f/1dL98VrpZfCuymVkim7kLwswsKRdgM7NEXIDNzBJxATYzS8QF2MwsERdgM7NEXIDNzBL5Lyxfad5ap3BsAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 360x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "######## Your code here ########\n",
    "model.Gaussian_noise.variance = 0.01\n",
    "model.plot(figsize=(5, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Now, let's generate more noisy data and try to fit model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Name : GP regression\n",
      "Objective : 33.66289801068251\n",
      "Number of Parameters : 3\n",
      "Number of Optimization Parameters : 3\n",
      "Updates : True\n",
      "Parameters:\n",
      "  \u001b[1mGP_regression.         \u001b[0;0m  |                value  |  constraints  |  priors\n",
      "  \u001b[1mrbf.variance           \u001b[0;0m  |   0.5656206123854732  |      +ve      |        \n",
      "  \u001b[1mrbf.lengthscale        \u001b[0;0m  |  0.14464727177409145  |      +ve      |        \n",
      "  \u001b[1mGaussian_noise.variance\u001b[0;0m  |  0.20850048348066721  |      +ve      |        \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f1c272f55c0>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " /home/yeahrmek/miniconda3/lib/python3.6/site-packages/matplotlib/figure.py:2267: UserWarning:This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 40\n",
    "X = np.linspace(0.05, 0.95, N).reshape(-1, 1)\n",
    "Y = -np.cos(np.pi * X) + np.sin(4 * np.pi * X) + \\\n",
    "    np.random.normal(loc=0.0, scale=0.5, size=(N, 1))\n",
    "\n",
    "kernel = GPy.kern.RBF(1)\n",
    "model = GPy.models.GPRegression(X, Y, kernel)\n",
    "model.optimize()\n",
    "print(model)\n",
    "model.plot(figsize=(5, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Now, let's fix noise variance to some small value and fit the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f1c272e3b70>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " /home/yeahrmek/miniconda3/lib/python3.6/site-packages/matplotlib/figure.py:2267: UserWarning:This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kernel = GPy.kern.RBF(1)\n",
    "model = GPy.models.GPRegression(X, Y, kernel)\n",
    "model.Gaussian_noise.variance.fix(0.01)\n",
    "model.optimize()\n",
    "model.plot(figsize=(5, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Approximate multi-dimensional function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rosenbrock(x):\n",
    "    x = 0.5 * (4 * x - 2)\n",
    "    y = np.sum((1 - x[:, :-1])**2 +\n",
    "                100 * (x[:, 1:] - x[:, :-1]**2)**2, axis=1)\n",
    "    return y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from matplotlib import cm\n",
    "from sklearn.metrics import mean_squared_error\n",
    "\n",
    "def plot_2d_func(func, n_rows=1, n_cols=1, title=None):\n",
    "    grid_size = 100\n",
    "    x_grid = np.meshgrid(np.linspace(0, 1, grid_size), np.linspace(0, 1, grid_size))\n",
    "    x_grid = np.hstack((x_grid[0].reshape(-1, 1), x_grid[1].reshape(-1, 1)))\n",
    "    y = func(x_grid)\n",
    "    fig = plt.figure(figsize=(n_cols * 6, n_rows * 6))\n",
    "    ax = fig.add_subplot(n_rows, n_cols, 1, projection='3d')\n",
    "    ax.plot_surface(x_grid[:, 0].reshape(grid_size, grid_size), x_grid[:, 1].reshape(grid_size, grid_size),\n",
    "                    y.reshape(grid_size, grid_size),\n",
    "                    cmap=cm.jet, rstride=1, cstride=1)\n",
    "    if title is not None:\n",
    "        ax.set_title(title)\n",
    "    return fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Here how the function looks like in 2D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plot_2d_func(rosenbrock)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "dim = 3\n",
    "x_train = np.random.rand(300, dim)\n",
    "y_train = rosenbrock(x_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task\n",
    "\n",
    "Try to approximate Rosenbrock function using RBF kernel.  \n",
    "**Hint**: if results are not good maybe it is due to bad local minimum. You can do one of the following things:\n",
    "1. Try to use multi-start by calling `model.optimize_restarts(n_restarts)` method of the model.\n",
    "2. Constrain model parameters to some reasonable bounds. You can do it for example as follows:\n",
    "`model.Gaussian_noise.variance.constrain_bounded(0, 1)`\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<paramz.optimization.optimization.opt_lbfgsb at 0x7f1c272d7dd8>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "######## Your code here ########\n",
    "kernel = GPy.kern.RBF(dim)\n",
    "model = GPy.models.GPRegression(x_train, y_train.reshape(-1, 1), kernel)\n",
    "model.optimize()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "MSE: 0.0003716835975778164\n"
     ]
    }
   ],
   "source": [
    "x_test = np.random.rand(3000, dim)\n",
    "y_test = rosenbrock(x_test)\n",
    "y_pr = model.predict(x_test)[0]\n",
    "\n",
    "mse = mean_squared_error(y_test.ravel(), y_pr.ravel())\n",
    "print('\\nMSE: {}'.format(mse))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Covariance functions\n",
    "\n",
    "Short info about covariance function can be printed using `print(k)`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  \u001b[1mrbf.       \u001b[0;0m  |  value  |  constraints  |  priors\n",
      "  \u001b[1mvariance   \u001b[0;0m  |    1.0  |      +ve      |        \n",
      "  \u001b[1mlengthscale\u001b[0;0m  |    1.0  |      +ve      |        \n"
     ]
    }
   ],
   "source": [
    "k = GPy.kern.RBF(1)\n",
    "print(k)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "You can plot the covariance function using `plot()` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f1c25f77b38>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " /home/yeahrmek/miniconda3/lib/python3.6/site-packages/matplotlib/figure.py:2267: UserWarning:This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.\n"
     ]
    },
    {
     "data": {
      "image/png": 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tmFT1WPPiKyJ2Ibu5KIv8ww9T/CsHR6MzsyGKHM1hnHEx/fBeaLcUJur41n0rAiKz81lrTRqV6V+2vsyWrY9CbS7AqnpjewYx0WVbcTn7j5yiW5cE8ob0cDqOYzolxHLlSN/0+Hfz9zmcxnS0gAVYfMaLyBf8t/ESaZ2yTYdrPPqNpHXf2mqav/ubDUNEn0Dd0KYBvwV2cWYObyYwUEQeUNXFQc5nIlCD18uS/MhZdv5iXTGyN50S3GwrLmff4Qr69ejidCTTQQIdejwNXKeqM1T16/7bdHwNdp4OfjwTiTbsPELZiWp6pyczIifN6TiOS4hzM9l/EYpdmhxdAhVgN76r1c52AIiuWfOm3SxsPPk2Nivi1n1rq8YFOxevLbJl66NIoD54L+JrIzmXM411+uK7CMNmQZgLVlvfwNJ1/nXfImjZ+Ys1fmgvUjrFs/dgBbsPnCA385xdXk2ECdSO8r+BOwEBLvffBLjL/zNjLsiKLQea1n0b0PszfZeiltvt4ro8XytOW7Y+egTsBK2q2/BdSmzMRVu4ugiAGeNznA0SgqbmZfH6B7tYsraYBz8/yoZnokCgfsBzAj1Ba/YxBqCiqpaPthxA5MzUK3PG6NzuZKQmUnqsik/2WkuUaBDoCPhmEWmpS4gAU9oxj4lgy9bvp97jZeyQnnTvmuR0nJDjcglT87L4+7vbWbSmiJH9052OZIIsUAF+uBXPsbw9gpjIt2D1XgBmTMh2NkgImzYum7+/u51384v5/hfHRP1FKpEuUDe0FhfkNKa1Dh2rYv3OI8THxjBldOSv+9ZWw7K6kZmRTElZJet3HmHsEOt5FclsDNh0iMam41dd2ofkRJtCfj4i0jQ+vmDVXofTmGCzMWDTIRqLyfRxNvshkBkT+vPi/AKWrtvHw7PHkmjL1kcsGwM2Qber5Dh7Sk+S0imOK0b0cjpOyMvu2YWR/dPZUniU99bv44bL+zsdyQSJjQGboGs8+r0uL4tYd3Q2Xr9QN13eny2FR3l75V4rwBHMTrGaoPI0eFnQdPFFtqNZwsnUsVnEuV3k7zjEoWPWqD1SWQE2QbWyoJSjJ6vp16MzlwzIcDpO2OicFMekUX1Rhfl2Mi5iBbUAi8h0EdkhIrtF5NEW9rtFRFRE8oKZx3S8eSsKAZg5cYBdWnuBbrrCN/TwzspC65AWodpUgEXk5yLyw8aVks+zTwzwLDADGAbMFpFh59ivM/AvwOq2ZDGhq7yihuWbSohxCTdOsHHMCzV+WE8yUhPZd+QUmwuPOh3HBEFbj4DXAB7gyRb2GQfsVtVCVa0D5gKzzrHfT4H/AVqa7mbC0ILVe2nwKleM6E16aqLTccJOjMvV1LTo7Y8LHU5jgqFNBVhV3wCeVtW7W9itD2d6CIOvsXuf5juIyBigr6q+09Lricj9IpIvIvllZWVtiWw6mKry5kd7AN/wg2mbG/0zIJasLaamzuNwGtPeAl0J95aIfKZtlYhcB2y8mBcWERfwK+ChQPuq6hxVzVPVvIwMO5ETDrYWHWPvwZN065zQtOqvuXD9e6cwPDuNqpp6Pth4rsVpTDgLdAQ8F3hPRB4TkVgR6S0irwA/A+4J8NgD+FbPaJTJmYU9AToDI4D3RaQImADMsxNxkWHeCt/R74wJObjdNtnmYjSejHvjo90OJzHtLdCKGH8DRgP98DVlXwm8C0xQ1XUBnnstkCsiOSISh28Zo3nNnvukqqararaqZgOrgJmqmt/md2NCQk2th0VrfItL2vDDxbt+XDbxsTHkbz/M/iOnnI5j2lFrDk2G4TuhtgaoBXrQupU0PMC3gUX4ivcrqlogIj8RkZltj2xC3bIN+6mqqWdk/3T6905xOk7Y65wU19Sg558f7nI4jWlPgcaAX8A3lewBVb0T39FwCrBJRKYFenJVna+qg1R1gKr+zL/tx6o67xz7Traj38jwpv+j8ufs6LfdfP7qXADe+riQuvoGh9OY9hLoCPgTYKyqrgRQ1SpV/VfgduBHwQ5nwk9h6UnW7zxCYry7aal1c/FG5KSRm5nKicpa3t+4P/ADTFgINAb8pKp+5s+tqm5R1auCF8uEq9fe3wnADRNyrO9vOxIRbr5qIAD//NBOxkWKQEMQfxCRkef5WScR+aqI3BWcaCbcVNXUM3+V74KBWyflOpwm8twwPoeEuBjydxym+HCF03FMOwg0BPEs8CMR2SYir4rIb0XkRRFZDnyMbyrZa0FPacLCwtV7qarxMDo3g4GZXZ2OE3GSk+K4flw2cOaThglvgYYgNqrqF4Gx+IrxcnxTyb6uqpeq6tOqWtsBOU2IU1Vefc9XFG6dNMjhNJHrtim+/7ZvrdhDZXW9w2nMxWrtDPnBqvq+qr6sqm+o6g4RuSmoyUxY2bi7jD2lvivfpozpG/gBpk0G9+3G6NzuVNV4eGel9YcId60twH8QkRGNd0RkNjYLwjQzd+l2AGZdOcBWvQiyO64ZDMAry3bg9VqbynDW2gJ8K/AXERkiIvcBDwAB5wGb6FBSdor3N5TgjnE1fUQ2wXP1qEx6dkti35FTrCwodTqOuQitKsCqWojvUuJ/ALcA01T1ZDCDmfAxd+kOvKpcPy6LjNQkp+NEPHeMi9sm+/7Q/d+yHQ6nMRcj0DS0LSKyWUQ245vt0A3IAVb7t5kod+p0XVPjnTuvG+pwmugx66qBxMfGsLLgILsPnHA6jmmjQD0d7ESbadE/P9xFda2HsUN6MqivTT3rKCmd4pk5cQCvvr+TlxZt5T+/eoXTkUwbBJqGVtzSraNCmtBU72lo+gh819QhDqeJPndNG0qMS1i0poiDxyqdjmPawBq1mjZbuKaIIyeqyemVwhUjejsdJ+r0SU9m6tgsGrzK35ZsdzqOaQMrwKZNPA1e/ji/AICvzBhuKx475J7rfevcvrF8NydO2bKK4cYKsGmTJfnF7D9yisyM5KZetabjDczsypUje1Nb38BcmxERdqwAmwvW4PXy4jufAHDvjBG4Y+zXyEn3TB8O+KakVVRZZ4BwYv9yzAVbtn4/RYcq6JXWiRsm5DgdJ+qNyu3O2CE9qayu529Ltjkdx1wAK8DmgjR4vbzw9hYAvjJ9uC24GSK+OesSAF5euoPjNhYcNuxfj7kgi1YXsaf0JD26JjWt1mucd8mADCaO6E11rYe/LNrqdBzTSlaATavV1jfw3JubAPjWzZcSF2tNd0LJN/xHwa++t5OjJ6odTmNaI6gFWESmi8gOEdktIo+e4+c/EJGt/sudl4qInU4PYa++t5ND5acZ2CeV6eOznY5jzjI0K40po/tSW9/AnLesU0A4CFoBFpEYfE3cZ+Bb2n62iAw7a7cNQJ6qXoKv18T/BiuPuTgVVbX8cb5v5sO3vzCKGJd9eApFD9x8KTEu4c2P9rCr5LjTcUwAwfxXNA7YraqFqloHzAVmNd9BVd9T1dP+u6uAzCDmMRfhTwsKqDhdx2WDethVbyEsu1cKt04ehFeVX72yDlXrFxzKglmA+wDN188u8W87n68BC871AxG5X0TyRSS/rKysHSOa1ig6eJKXl+5ABL5z62i76i3E3fe5kXRJiiN/+2E+3FTidBzTgpD4HCkiXwLygCfO9XNVnaOqeaqal5GR0bHhopyq8j8vr8XT4GXWlQMZnp3mdCQTQEqneO6f6Tsh99Sr66mrb3A4kTmfYBbgA0DzxcEy/ds+RUSuAx4DZtoCn6FnSX4x+dsPk9Ipjgc/P8rpOKaVbrk6l5xeXSgpq+TPCwucjmPOI5gFeC2QKyI5IhKHb0WNec13EJHRwO/xFd8jQcxi2qCqpp6nXl0PwINfGE1qcrzDiUxrud0ufnjnOABenF/AnlJr2h6KglaAVdUDfBtYBGwDXlHVAhH5iYjM9O/2BJAMvCoiG0Vk3nmezjjgN69voOxENcOz05g1cYDTccwFumxwDz5/1UA8DV5+9pfVNHi9TkcyZwm0IsZFUdX5wPyztv242ffXBfP1TdutLCjl9Q924Y5x8djd43G57MRbOPruLaNZvvkAWwqP8tr7u7jdv6KyCQ0hcRLOhJaKqlp++udVANw/cyS5mbbUULhKTorjh3eOBeCZf2yg6FCFw4lMc1aAzWc8MTefshPVjOyfzpennX3tjAk3k0f3Zfr4bGrqGnjsDx/ZrIgQYgXYfMpbH+9h4eoi4mNjePzey63Xb4T44Z3j6JOezM79x/nNPzY4Hcf42b8u02THvnL+529rAXhk9lj69ejicCLTXpITY/nZfROJcQlzl+6wCzRChBVgA/jGfR/53XJq6xuYdeUAZl5psx4izfCc9Ka53D9+4WMKS086nMhYATZ4PF7+4/kVlB6tZGhWNx6ePdbpSCZI7po6lGvH9KOqpp4fPPO+LeTpMCvAUU5V+dlfV7Oy4CApneL5xTeuIt76/EYsl0t4/N7LGZrVjQNHK3nkd8up99hJOadYAY5yz72xibc/LiQhLoanvjOZ3unJTkcyQZYQ7+aXD0wiPSWRDbuO8B/Pr8DTYBdpOMEKcBT76+Jt/HFBATEu4RffuIoR/dOdjmQ6SPeuSTz1nckkJ8aybP1+Hv/jSrtSzgFWgKOQqvL821t4+jVfn4d///J4Jo5sqVOoiUSD+3Xj6e9OISnezaI1RXa5sgOsAEcZVeWZf27k9/M24xLhR/dMYKb1eYhalwzI4MnvTCY+Noa3Pi7k0d8tp6bO43SsqGEFOIrU1Hr40Qsr+MvCrcS4hJ9+/QorvoYxg3rwm+9dQ+ekON7fWMIDv1pqsyM6iBXgKHGovIr7nljCojXFJMW7eeKBq5k2NtvpWCZEjM7tzvOPTKNntyS2FB7lnp8vpGDvUadjRTwrwFFg2fp9fPm/FrB9Xzl90pN54dHrueoSW37PfFr/3im8+Oj1DM3qRumxKr7+v0t4eel2W1cuiCTc/uPm5eVpfn6+0zHCQkVVLb+cm8+C1UUATBjWi/+6byIpnayxujm/uvoGfv36Bv5v2Q4Axg7pyaN32aXpF0JE1qlqXsD9rABHHk+Dl3kf7eG5NzdxorKW+NgYvnvraG6dNMj6+ppWW7Z+Hz9/aTUnq+qIc7u494YRfGnqUBLig9pGPCJYAY5CXq/ywaYS5szbzO4DviVoRudm8NjdE8iyoxfTBsdP1fD0axt4Z2UhAOkpiXz1xhHcfOUAYt12xeT5WAGOIjW1HhavLealxVubGm73TuvEd28dwzVj+toy8uai5W8/xNOvbWD7vnLAdyHHbZMHcfOVA0jtnOBwutBjBTjCeb3Klr1Hmb+ykEVriqmqqQegZ7ckvjRtGDdfNdB6Oph2paq8t34/v5u3mb0HfZ3U4mNjmDw6k2ljs7l8eC87KvazAhyBjlVUs3FXGau3HuSDTSWUV5yZqzkiJ41bJg1i+rhs3G6b3GKCx+tVVm09yCvLdrDik9Km7V2S4pgwvBeXD+/N+GE9yUhNcjCls0KiAIvIdOBpIAZ4XlV/cdbP44G/AJcBx4DbVbWopeeMlgJ84lQNe0pPUnjwJNuLy9m46wj7jpz61D690joxZUxfZk4cwIDeqQ4lNdHswNFKFq8tYvGa4qbzDo16dE1iRE46w3PSGJrVjeyeKaSlJETFkJjjBVhEYoCdwFSgBFgLzFbVrc32eQC4RFW/KSJ3AJ9X1dtbet5wLsCqyulaD5XV9Zw6XUfl6TqOnqzm8PHTHPHfDh8/zYGySsrPcSVSYrybkf3TGZXbnasv7cOgzK5R8ctswkPx4QpWFRzk409K2bT7CFU1n72kOSneTb8eXejbvTMZqYmkdUkgPSWRNP8tpVMcnRJiSYx3h/XvdmsLcDDnk4wDdqtqoT/QXGAWsLXZPrOAx/3fvwY8IyKi7fhXYVfJcVZsKUVVUQWvKgqo1/fVqwot/sy/XfnUc4Dvo5gC9R4v9Z4G6uobqPN4qfM0UF/v/+rx+oru6Toqq+ubHhtIUrybnF4p9O+dwsA+qVya253BmV1teMGErKweXcjq0YXbrxmM16sUHaqgoOgoBXuPsXP/cfYdruBkVR3b95U3ncw7HxFIio+lU4KbTomxJMXHEhfrwh0TQ6zbRWyMi1i3ixj/16b7LhcigIBLBAFEBBH/V0BcZ7a7fN/gEhD077PqAAAFU0lEQVSk6bHNDc9OZ9zQnkH5bxbMAtwH2N/sfgkw/nz7qKpHRE4CaUC7XQO5rbicZ/+5sb2e7qIlxMXQOSmO5MQ4khNjSUtJpEfXJLqnJtK9axLduybRK60TPbp2sjm7Jmy5XEL/3r4DiM9dcabfyInKWvYdrqCkrJJjFdUcPVnNsZPVHD1Rw7GKak6drqOqpp6augaqaup9J5dPVDv4TuDOqUPCsgC3GxG5H7gfoF+/fhf02IF9Url7+jAE/1/Exr+EZ/01/PTPfPc/9Ve02X5N2/1/Nd1uF3FuF3HuGGJj/V/dLuJjY4h1x5AY76ZzYizJiXF2BGuiWmpyPKnJGVwyIKPF/TwNXqprPU1F+HSNh3r/J0pPg9f3qbPhzPeeZvd9H1zP+vSKol7/12afZpt/Cvb6t59t1MDuQfqvEdwCfADo2+x+pn/bufYpERE3kILvZNynqOocYA74xoAvJMSw7DSGZaddyEOMMQ5zx7jonBRH56Q4p6MEVTAPx9YCuSKSIyJxwB3AvLP2mQfc4//+VmBZe47/GmNMKAvaEbB/TPfbwCJ809BeVNUCEfkJkK+q84AXgJdEZDdQjq9IG2NMVAjqGLCqzgfmn7Xtx82+rwFuC2YGY4wJVXZGyBhjHGIF2BhjHBJ2vSBEpAwo7uCXTacd5yaHAXu/kS3a3i90/HvOUtWW59oRhgXYCSKS35rLCiOFvd/IFm3vF0L3PdsQhDHGOMQKsDHGOMQKcOvMcTpAB7P3G9mi7f1CiL5nGwM2xhiH2BGwMcY4xAqwMcY4xArwBRCRh0RERSTd6SzBJiJPiMh2EdksIv8UkYhc80hEpovIDhHZLSKPOp0nmESkr4i8JyJbRaRARP7F6UwdQURiRGSDiLztdJazWQFuJRHpC0wD9jmdpYMsAUao6iX4lpb6N4fztDv/slnPAjOAYcBsERnmbKqg8gAPqeowYALwYIS/30b/AmxzOsS5WAFuvSeBR/D1cI54qrpYVRsX9VqFr59zpGlaNktV64DGZbMikqoeVNX1/u9P4StKfZxNFVwikgncCDzvdJZzsQLcCiIyCzigqpuczuKQrwILnA4RBOdaNiuiC1IjEckGRgOrnU0SdE/hO3DyOh3kXMJiSaKOICLvAuda+Okx4N/xDT9ElJbes6q+6d/nMXwfXf/WkdlM8IhIMvA68D1VrXA6T7CIyE3AEVVdJyKTnc5zLlaA/VT1unNtF5GRQA6wyb9MdiawXkTGqeqhDozY7s73nhuJyFeAm4BrI3SlktYsmxVRRCQWX/H9m6r+w+k8QTYRmCkiNwAJQBcR+auqfsnhXE3sQowLJCJFQJ6qRnQ3KRGZDvwKmKSqZU7nCQb/OoQ7gWvxFd61wJ2qWuBosCAR3xHEn4FyVf2e03k6kv8I+F9V9SanszRnY8DmfJ4BOgNLRGSjiPzO6UDtzX+SsXHZrG3AK5FafP0mAl8GrvH/P93oPzo0DrEjYGOMcYgdARtjjEOsABtjjEOsABtjjEOsABtjjEOsABtjjEOsAJuo5O8MtldEuvnvd/Xfz3Y2mYkmVoBNVFLV/cBzwC/8m34BzFHVIsdCmahj84BN1PJflrsOeBG4DxilqvXOpjLRxHpBmKilqvUi8jCwEJhmxdd0NBuCMNFuBnAQGOF0EBN9rACbqCUio4Cp+FaH+L6I9HI4kokyVoBNVPJ3BnsOX0/cfcATwC+dTWWijRVgE63uA/ap6hL//d8CQ0VkkoOZTJSxWRDGGOMQOwI2xhiHWAE2xhiHWAE2xhiHWAE2xhiHWAE2xhiHWAE2xhiHWAE2xhiH/D9DBuNJ37PMhgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 360x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k.plot(figsize=(5, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## More \"complex\" functions\n",
    "The most popular covariance function is RBF. However, not all the functions can be modelled using RBF covariance function. For example, approximations of discontinuous functions will suffer from oscillations, approximation of curvy function may suffer from oversmoothing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def heaviside(x):\n",
    "    return np.asfarray(x > 0)\n",
    "\n",
    "\n",
    "def rastrigin(x):\n",
    "    \"\"\"\n",
    "    Parameters\n",
    "    ==========\n",
    "        x : ndarray - 2D array in [0, 1]\n",
    "    \n",
    "    Returns\n",
    "    =======\n",
    "        1D array of values of Rastrigin function\n",
    "    \"\"\"\n",
    "    scale = 8  # 10.24\n",
    "    x = scale * x - scale / 2\n",
    "    y = 10 * x.shape[1] + (x**2).sum(axis=1) - 10 * np.cos(2 * np.pi * x).sum(axis=1)\n",
    "    return y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plot_2d_func(rastrigin, 1, 2, title='Rastrigin function')\n",
    "\n",
    "x = np.linspace(-1, 1, 100)\n",
    "y = heaviside(x)\n",
    "\n",
    "ax = fig.add_subplot(1, 2, 2)\n",
    "ax.plot(x, y)\n",
    "ax.set_title('Heaviside function')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example of oscillations\n",
    "As you can see there are oscillations in viscinity of discontinuity because we are trying to approximate\n",
    "discontinuous function using infinitily smooth function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.2, 1.2)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " /home/yeahrmek/miniconda3/lib/python3.6/site-packages/matplotlib/figure.py:2267: UserWarning:This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "X = np.random.rand(30, 1) * 2 - 1\n",
    "y = heaviside(X)\n",
    "\n",
    "k = GPy.kern.RBF(input_dim=1, variance=1., lengthscale=1.)\n",
    "\n",
    "m = GPy.models.GPRegression(X, y, k)\n",
    "m.optimize()\n",
    "m.plot(figsize=(5, 3))\n",
    "plt.ylim([-0.2, 1.2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example of oversmoothing\n",
    "Actually, the GP model only approximates trend of the function.\n",
    "All the curves are treated as noise.\n",
    "The knowledge about this (in fact there is some repeated structure) should be incorporated into the model via kernel function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "\n",
    "X = np.random.rand(300, 2)\n",
    "y = rastrigin(X)\n",
    "\n",
    "k = GPy.kern.RBF(input_dim=2)\n",
    "\n",
    "m = GPy.models.GPRegression(X, y.reshape(-1, 1), k)\n",
    "m.optimize()\n",
    "fig = plot_2d_func(lambda x: m.predict(x)[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Covariance functions in GPy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Popular covariance functions: `Exponential`, `Matern32`, `Matern52`, `RatQuad`, `Linear`, `StdPeriodic`. \n",
    "\n",
    "* Exponential:\n",
    "$$\n",
    "k(x, x') = \\sigma^2 \\exp \\left (-\\frac{r}{l} \\right), \\quad r = \\|x - x'\\|\n",
    "$$\n",
    "\n",
    "* Matern32\n",
    "$$\n",
    "k(x, x') = \\sigma^2 \\left (1 + \\sqrt{3}\\frac{r}{l} \\right )\\exp \\left (-\\sqrt{3}\\frac{r}{l} \\right )\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "* Matern52\n",
    "$$\n",
    "k(x, x') = \\sigma^2 \\left (1 + \\sqrt{5}\\frac{r}{l} + \\frac{5}{3}\\frac{r^2}{l^2} \\right ) \\exp \\left (-\\sqrt{5}\\frac{r}{l} \\right )\n",
    "$$\n",
    "\n",
    "* RatQuad\n",
    "$$\n",
    "k(x, x') = \\left ( 1 + \\frac{r^2}{2\\alpha l^2}\\right )^{-\\alpha}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "* Linear\n",
    "$$\n",
    "k(x, x') = \\sum_i \\sigma_i^2 x_i x_i'\n",
    "$$\n",
    "\n",
    "* Poly\n",
    "$$\n",
    "k(x, x') = \\sigma^2 (x^T x' + c)^d\n",
    "$$\n",
    "\n",
    "* StdPeriodic\n",
    "$$\n",
    "k(x, x') = \\sigma^2 \\exp\\left ( -2 \\frac{\\sin^2(\\pi r)}{l^2}\\right )\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Combination of covariance functions\n",
    "\n",
    "* Sum of covariance function is a valid covariance function:\n",
    "\n",
    "$$\n",
    "k(x, x') = k_1(x, x') + k_2(x, x')\n",
    "$$\n",
    "\n",
    "* Product of covariance functions is a valid covariance funciton:\n",
    "$$\n",
    "k(x, x') = k_1(x, x') k_2(x, x')\n",
    "$$\n",
    "\n",
    "### Combinations of covariance functions in GPy\n",
    "\n",
    "In GPy to combine covariance functions you can just use operators `+` and `*`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's plot some of the combinations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x432 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "covariance_functions = [GPy.kern.Linear(input_dim=1), GPy.kern.StdPeriodic(input_dim=1), GPy.kern.RBF(input_dim=1, lengthscale=1)]\n",
    "operations = {'+': lambda x, y: x + y, '*': lambda x, y: x * y}\n",
    "\n",
    "figure, axes = plt.subplots(len(operations), len(covariance_functions), figsize=(9, 6))\n",
    "\n",
    "import itertools\n",
    "axes = axes.ravel()\n",
    "count = 0\n",
    "for j, base_kernels in enumerate(itertools.combinations(covariance_functions, 2)):\n",
    "    for k, (op_name, op) in enumerate(operations.items()):\n",
    "        kernel = op(base_kernels[0], base_kernels[1])\n",
    "        kernel.plot(ax=axes[count])\n",
    "        axes[count].set_title('{} {} {}'.format(base_kernels[0].name, op_name, base_kernels[1].name),\n",
    "                              fontsize=14)\n",
    "        count += 1\n",
    "figure.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Additive kernels\n",
    "\n",
    "One of the popular approach to model the function of interest is\n",
    "$$\n",
    "f(x) = \\sum_{i=1}^d f_i(x_i) + \\sum_{i < j} f_{ij}(x_i, x_j) + \\ldots\n",
    "$$\n",
    "\n",
    "**Example**: $\\quad f(x_1, x_2) = f_1(x_1) + f_2(x_2)$  \n",
    "To model it using GP use additive kernel $\\quad k(x, y) = k_1(x_1, y_1) + k_2(x_2, y_2)$.\n",
    "\n",
    "More general - add kernels each depending on subset of inputs\n",
    "$$\n",
    "k(x, y) = k_1(x, y) + \\ldots + k_D(x, y),\n",
    "$$\n",
    "where, for example, $k_1(x, x') = k_1(x_1, x_1'), \\; k_2(x, x') = k_2((x_1, x_3), (x_1', x_3'))$, etc.\n",
    "\n",
    "Here is an example of ${\\rm RBF}(x_1) + {\\rm RBF}(x_2)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k1 = GPy.kern.RBF(1, active_dims=[0])\n",
    "k2 = GPy.kern.RBF(1, active_dims=[1])\n",
    "\n",
    "kernel = k1 + k2\n",
    "\n",
    "x = np.meshgrid(np.linspace(-3, 3, 50), np.linspace(-3, 3, 50))\n",
    "x = np.hstack((x[0].reshape(-1, 1), x[1].reshape(-1, 1)))\n",
    "z = kernel.K(x, np.array([[0, 0]]))\n",
    "\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from matplotlib import cm\n",
    "\n",
    "figure = plt.figure()\n",
    "ax = figure.add_subplot(111, projection='3d')\n",
    "ax.plot_surface(x[:, 0].reshape(50, 50), x[:, 1].reshape(50, 50), z.reshape(50, 50), cmap=cm.jet)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Kernels on arbitrary types of objects\n",
    "\n",
    "Kernels can be defined over all types of data structures: text, images, matrices, graphs, etc. You just need to define similarity between objects.\n",
    "\n",
    "#### Kernels on categorical data\n",
    "\n",
    "* Represent your categorical variable as a by a one-of-k encoding: $\\quad x = (x_1, \\ldots, x_k)$.\n",
    "* Use RBF kernel with `ARD=True`: $\\quad k(x , x') = \\sigma^2 \\prod_{i = 1}^k\\exp{\\left ( -\\dfrac{(x_i - x_i')^2}{\\sigma_i^2} \\right )}$. The lengthscale will now encode whether the rest of the function changes.\n",
    "* Short lengthscales for categorical variables means your model is not sharing any information between data of different categories. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 2 Sampling from GP\n",
    "\n",
    "So, you have defined some complex kernel.\n",
    "You can plot it to see how it looks and guess what kind of functions it can approximate.\n",
    "Another way to do it is to actually generate random functions using this kernel.\n",
    "\n",
    "GP defines distribution over functions, which is defined by its *mean function* $m(x)$ and *covariance function* $k(x, y)$: for any set $\\mathbf{x}_1, \\ldots, \\mathbf{x}_N \\in \\mathbb{R}^d \\rightarrow$ $\\left (f(\\mathbf{x}_1), \\ldots, f(\\mathbf{x}_N) \\right ) \\sim \\mathcal{N}(\\mathbf{m}, \\mathbf{K})$,\n",
    "where $\\mathcal{m} = (m(\\mathbf{x}_1, \\ldots, \\mathbf{x}_N)$, $\\mathbf{K} = \\|k(\\mathbf{x}_i, \\mathbf{x}_j)\\|_{i,j=1}^N$.\n",
    "\n",
    "Sampling procedure:\n",
    "\n",
    "1. Generate set of points $\\mathbf{x}_1, \\ldots, \\mathbf{x}_N$.\n",
    "2. Calculate mean and covariance matrix $\\mathcal{m} = (m(\\mathbf{x}_1, \\ldots, \\mathbf{x}_N)$, $\\mathbf{K} = \\|k(\\mathbf{x}_i, \\mathbf{x}_j)\\|_{i,j=1}^N$.\n",
    "3. Generate vector from multivariate normal distribution $\\mathcal{N}(\\mathbf{m}, \\mathbf{K})$.\n",
    "\n",
    "Below try to change RBF kernel to some other kernel and see the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k = GPy.kern.Matern52(input_dim=1, lengthscale=0.3)\n",
    "\n",
    "X = np.linspace(0, 5, 500).reshape(-1, 1)\n",
    "\n",
    "mu = np.zeros(500)\n",
    "C = k.K(X, X)\n",
    "\n",
    "Z = np.random.multivariate_normal(mu, C, 3)\n",
    "\n",
    "plt.figure()\n",
    "for i in range(3):\n",
    "    plt.plot(X, Z[i, :])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Task\n",
    "\n",
    "Build a GP model that predicts airline passenger counts on international flights."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAUYAAADFCAYAAAAohFsyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAGOBJREFUeJzt3X+Q3HV9x/Hn+3KJilJyJiEGLsmBCThAiyRXTAerRJQxiIWCBBwqAUPTH5mODJ0R7HSwVTuDtlbilMFmwDZUfgoyRIpKiSCVGuAuMsgv05DJkTsDSeBCbYNccvfuH9/PXva+2R/f3f3u7nd3X4+Zm9v97nf3Ptm7feXz8/sxd0dERA7panYBRESyRsEoIhKjYBQRiVEwiojEKBhFRGIUjCIiMQpGEZEYBaOISIyCUUQkprvZBQCYPXu29/X1NbsYItJmBgcH97r7nEqfl4lg7OvrY2BgoNnFEJE2Y2ZD1TxPTWkRkRgFo4hIjIJRRCRGwSgimTM4NMqNj2xjcGi0KT8/E4MvIiI5g0OjXHrzZsYOTjCju4vbrlzG0oU9DS2Daowikimbt7/G2MEJJhwOHJxg8/bXGl4GBaOIZMqy42cxo7uLaQbTu7tYdvyshpchUVPazGYCNwOnAA58FvglcBfQB+wAVrr7qJkZsA44B9gPXO7uW1IvuYi0paULe7jtymVs3v4ay46f1fBmNCSvMa4Dfuju7wNOBV4ArgU2uftiYFO4D7ACWBy+1gA3pVpiEWl7Sxf2sHb5oqaEIiQIRjM7CvgQcAuAu4+5+z7gPGBDOG0DcH64fR5wq0c2AzPNbF7qJRcRqZMkNcbjgD3Av5jZz83sZjN7JzDX3XeFc14B5obbxwI7854/HI5NYWZrzGzAzAb27NlT/b9ARCRlSYKxG1gC3OTupwH/x6FmMwAe7cFa0T6s7r7e3fvdvX/OnIrXeIuI1E2SYBwGht39iXD/HqKgfDXXRA7fd4fHR4D5ec/vDcdERFpC2WB091eAnWZ2Yjh0FvA8sBFYFY6tAu4PtzcCl1lkGfBGXpNbRCTzkq58+QvgNjObAWwHriAK1bvNbDUwBKwM5z5INFVnG9F0nStSLbGISJ0lCkZ3fxroL/DQWQXOdWBtjeUSEWkarXwRkcxq1sUkdBEJEcmkZl5MQjVGEcmkZl5MQsEoIpnUzItJqCktIpnUzItJKBhFJLOWLuzJ9NV1REQ6hoJRRCRGwSgiEqNgFBGJUTCKSE2avdVpPWhUWkSqloWtTutBNUYRqVoWtjqtBwWjiFQtC1ud1oOa0iJStUatThkcGm3oChgFo4hUJT+s1i5fVNef0+h+TAWjiFSskWFVqB+z3sGoPkYRqVgjB12a0Y+pGqOIVCwXVgcOTtQ9rJpxlR2Ltmgpc5LZDuDXwDhw0N37zezdwF1AH7ADWOnuo2ZmwDqiDbH2A5e7+5ZSr9/f3+8DAwM1/DNEpNEaPSBSDTMbdPdC+1WVVEmNcbm77827fy2wyd2vN7Nrw/1rgBXA4vD1AeCm8F1E2kizLgnWCLX0MZ4HbAi3NwDn5x2/1SObgZlmNq+GnyMi0lBJg9GBh8xs0MzWhGNz3X1XuP0KMDfcPhbYmffc4XBsCjNbY2YDZjawZ8+eKoouIlIfSZvSH3T3ETM7GvgPM3sx/0F3dzMr31k59TnrgfUQ9TFW8lwRkXpKVGN095HwfTdwH3A68GquiRy+7w6njwDz857eG46JiLSEssFoZu80syNzt4GzgWeBjcCqcNoq4P5weyNwmUWWAW/kNblFRDIvSVN6LnBfNAuHbuB2d/+hmT0F3G1mq4EhYGU4/0GiqTrbiKbrXJF6qUVE6qhsMLr7duDUAsdfA84qcNyBtamUTkSkCbQkUEQkRsEoIhKjYBQRiVEwiojEKBhFRGIUjCIiMQpGkQ7Rjvs/14suVCvSAdp1/+d6UY1RpAOkuRVBJ9Q8VWMUaXODQ6OM7HuT7mldjI/XthVBp9Q8FYwiTdKIrQHyg6y7y7jk9AVcsKS36p/XjB37mkHBKNIEjap55QfZ+IRzzMx31PRzGrkJVjMpGEWaoFE1r7SDrBk79jWDglGkCRpV86pHkLXzJlg5ibZPrTdtnyqdqBW2H623er8Hjdg+VURSVO+aV9aDN8sj3ApGkTaU5dDJKTa3MgthrmAUaUOtMK2m54gZdJkBzvTuLnqOmJGZMNfKF5E2lBvcmWZkclrN4NAoX3rgOcYnnC4zrjv3ZEb3j6W2OqdWqjGKtKGsT6vJ1WgdcHdG949lao5k4mA0s2nAADDi7uea2XHAncAsYBD4jLuPmdnbgFuBpcBrwMXuviP1kotISVmeVlMoBLMU5pXUGD8HvAD8Vrj/VeAb7n6nmX0LWA3cFL6PuvsiM7sknHdximUWkRZXLASzEuaJ+hjNrBf4BHBzuG/AR4B7wikbgPPD7fPCfcLjZ4XzRUQmLV3Yw9rlizIRhHFJB19uAD4PTIT7s4B97n4w3B8Gjg23jwV2AoTH3wjnT2Fma8xswMwG9uzZU2XxRUTSVzYYzexcYLe7D6b5g919vbv3u3v/nDlz0nxpEZGaJOljPAP4AzM7B3g7UR/jOmCmmXWHWmEvMBLOHwHmA8Nm1g0cRTQIIyKS+RU5kKDG6O5fcPded+8DLgF+7O6XAo8AnwqnrQLuD7c3hvuEx3/sWViQLSJNl1uR8/WHfsmlN2/O7FXAa5ngfQ1wtZltI+pDvCUcvwWYFY5fDVxbWxFFpF0UWwaYte0SKprg7e6PAo+G29uB0wuc8xvgohTKJiJtptD8xSyu69bKF5Ema4U+t7QUmr944yPbMreuW8Eo0kRZrC3VW3wSd5aWAuYoGEWaqBWugpNUtTXfLC0FzFEwijRRFmtL1ai15puVpYA5CkaRJspibamaml+Smm8r9aUqGEWaLK3aUi54eo6YMXkZr0pft9qaX7mab6v1pSoYRdpALnjeOhBd47DLqCqAqu3zLFfzbbW+VAWjSBvIv/ArUHUA1dLnWarm22p9qQpGkTaQC56xAxNMENUYqwmgevV5ZrEvtRTtKy3SJtLoY2w32ldapEMUG92t15SXVhpNTouCUaRFDA6Ncu+WYe4ZHObgeGNGd1ttNDktCkaRjChVM4uPOkNjNqlvtdHktCgYRTIgv2bW3WVc1D+fC5b0ToZQfNTZoOpN6itpGrfaaHJaFIwiGZBfMxsbd25/4mXu3TI8GXT5ATUtLzgrrdFV2jRutdHktCgYRTIgF3y5prIzNehKBVQlNbpSQRqvSebfX7t8UR3/9dmjYBTJgFzw5QZXxscPD7pCo86V1uiKNY3jNcnrzj2ZLz3wXMcNuuQoGEUyIhd8F4Ymcs8RMyYHV8o1d5OGVrEgjdckf/Dsro4cdMlRMIpkTC6AyvUF1nL9w/j58ZrkilPm8dSO1ztu0CVHwSh10YmTgtM0ZTDmwAQ3PLyVqz56wpT+wFrnF8Z/R/Ga5InvObJon2O5AZ5qnpclZYPRzN4OPAa8LZx/j7t/0cyOA+4k2iFwEPiMu4+Z2duAW4GlRPtJX+zuO+pUfsmgTp0UnKb42ufHt+3lqR2vT76Xtc4vLPY7KraSJunvND7t6MwTj+bRrXsaNiE9LUm2T30L+Ii7nwq8H/i4mS0Dvgp8w90XAaPA6nD+amA0HP9GOE86SLEtMuspa9tv1ipXgztj8Wy6jMPey1xwTqvyYhGFaqSl3rukv9P4tKOHnn+14X8LaSgbjB7533B3evhy4CPAPeH4BuD8cPu8cJ/w+FlmZqmVWDKv1g9tpVplE/dKLV3Yw1UfPaHge5kLzqvPPrGqWljud9QFkzXSUu9d0t9p7rz4Bz43Ib1V+ioTXV3HzKYRNZcXATcCfw9sDrVCzGw+8AN3P8XMngU+7u7D4bGXgA+4+97Ya64B1gAsWLBg6dDQUHr/Kmm6RvYr3fjINr7+0C+ZcJhmcPXZJ7bVvLt6vZeDQ6Pc8PBWHt+2N9F7V0kfY/60o2kFVvI0Sl2vruPu48D7zWwmcB/wvkp/UIHXXA+sh+iyY7W+nmRLIzc3avdla/V6L3M10qSjz0nLEZ921EqDLjkVjUq7+z4zewT4PWCmmXW7+0GgFxgJp40A84FhM+sGjiIahBGpi05dtpaGer53Wdv5rxJJRqXnAAdCKL4D+BjRgMojwKeIRqZXAfeHp2wM938WHv+xZ+FquFJSK06pyNfKH8Jm03t3uCQ1xnnAhtDP2AXc7e4PmNnzwJ1m9hXg58At4fxbgH8zs23A68AldSi3pEjTa0SmKhuM7v4McFqB49uB0wsc/w1wUSqlk4bo1GvuiRSTZB6jtLlGT68RyTotCRQNXojEKBgFyH4HfKsPDklrUTBKKuoZXBockkZTMErN6h1clQwOqWYpaVAwSs2SBFctgZV0ZYtqlpIWBaPUrFxw1RpYSQeHNO1I0qJglJrkaoLXnXsyo/vHDrscf+5CBbUGVpLBoXZfMy2No2CUqpXbQCl3P7fzXVeK8yQLNc017UjSomCUqpXbQCl334lWEpyxaPaUy/MXkqQvslTTPOvTjqQ1aOWLVC2+YmbFKfOK3p8xvStRKCa54GwzrhAunUU1xozL8vSTJBsoxe+XknTwRH2JUm8KxgxrheknpTZQKnS/lKSBp75EqTcFY4a14/STUjXgSgJPfYlSTwrGDGtEk7GRewAnqQGXC7wsdy1I+1AwZli9m4zlpts0c2lfkvKW2ttY4Sm1UDBmXD2bjOWm2+QHVxphU2sNOOnSw6z3y0r2KRg7WDyoVpwyb3LHuGldxq/2vTk5ZSaNsKm1BpwkWNuxX1YaT8HYIZKuFDnxPUdO7gl8x5Mvc++WYS5c0pta2FRaA46XO17e+OOayiNpSLJL4HzgVmAu4MB6d19nZu8G7gL6gB3ASncfNTMD1gHnAPuBy919S32KL0lUslJk6cIeNm9/jYPjh4LQYTJs8muS9a6JFSt3fvO+0OOayiO1SrLy5SDwl+5+ErAMWGtmJwHXApvcfTGwKdwHWAEsDl9rgJtSL7VUpNKVIvEVLRcu6eW2K5dx8ekLwIw7nny55MqURpW72ONLF/awdvkihaJULckugbuAXeH2r83sBeBY4DzgzHDaBuBR4Jpw/Nawl/RmM5tpZvPC60gTVNq8LFbritck691/V67cajZLvVTUx2hmfURbqT4BzM0Lu1eImtoQhebOvKcNh2NTgtHM1hDVKFmwYEGFxZZKJOmbK/Sc+PFGB1G5ZrGazVIvFlXsEpxo9i7gJ8Dfufv3zGyfu8/Me3zU3XvM7AHgenf/aTi+CbjG3QeKvXZ/f78PDBR9WFJWy5SWtOYI5l6n54gZjO4fO+z1NBdR0mBmg+7eX+nzEtUYzWw6cC9wm7t/Lxx+NddENrN5wO5wfASYn/f03nBMMqKWKS1pzKvMBXP+dRrzA1pzEaXZyg6+hFHmW4AX3P0f8x7aCKwKt1cB9+cdv8wiy4A31L+YLfHBlUb3zeWCOddWiQ+e6LJi0mxJaoxnAJ8BfmFmT4djfwVcD9xtZquBIWBleOxBoqk624im61yRaokzqtamX6XPr+XnNbtvLhfMYwcmmODwK3trUEWaLXEfYz21eh9jrU2/Sp+fhT7CWqmPURqhrn2MUlqty9Aq3Te51OZSpQIlS3135foqdVkxaSYFYwpqafoNDo0ysu9Nuqd1MT6ebN/kYptLlQu+LK8jVg1RskTBWKVya3iTvkYuyLq7jEtOX8AFS3qLXkorV1MstrlUueDLat9dlmqyIqBgrEq5NbxJ5QfZ+IRzzMx3FA3FQtNb4ptLlQu+Zg+6FJPlmqx0JgVjFfI/yGMHJrjh4a1ld8ArpFSQ5ddI86e3lNqGNEnwpdV3l2bTN6s1WelcCsYqxKebPL5tL0/teH1KEzDJlgHFgqzQlbXzg6NQKOa//trliwoeT6sWlnbTN6s1WelcHRWMaYVE7oN8w8NbeXzb3sOagKW2DOjuMi7qnz/ZlxivwRUadR7dP1YyOIoFVRoBVug9q0fTV6PQkiUdE4zVhkSxMF26sIerPnrC5BWv85uApbYMGBt3bn/iZb47sHNKQOaXsdCoc6ngKBZU9dpjRU1faXcdE4zVhES5MC3WBCy2ZUAu8JxDAXnvluHJ103alxgvY7HpPvXaY0VNX2l3HROM1YREkjAtVJMrt2VA7qrYztTXjZcxSSiWmu5Ta4CVes/U9JV21tbBWOtcw1pqXPHgyN2/cEnvZEDGa3iVlrHUdJ9igzGVUM1QOlXbBmOpuYaDQ6Pc+Mi2RB/2C5b0YuF7GsGQH5DF+i6T/pxiwZ3mqLFqhtKJ2jYYi801hGRbgcbD5YIlvamWL43AKVaj04Rpkdq0RTAWGjkuNtcw6Vag8XC5d8twyavBlCpLPRUKWI0ai9Sm5YMxPgCRPwWm0FzD/K1AS4VGfrhM67IpgybxK04XKksz1/yqb1CkNi0fjFOazAWmwMTnGl64pLdo/15OrtZ33bknM7p/jF/te5M7nny54BWns3r1GvUNilSvpYMxfw5f/hSY+PrlQrWnYoMwhWp9APduGS56xekcNWFF2kPLBmO8Cf2xk+by6NY9HDxYeP1y0mV0hWp9a5cvmgzXUn2MasKKtIeWDMb4euLxCefU+TP5kw+/t+j65bhizd5itb6kTVM1YUVaX8sFY7n1xMXWL8cVCsB432IatT5dmVqk9ZQNRjP7NnAusNvdTwnH3g3cBfQBO4CV7j4atlpdR7RL4H7gcnffkmaBy60nTtqcjZ8HyeY3ViIro9QiUpmy+0oD/wp8PHbsWmCTuy8GNoX7ACuAxeFrDXBTOsU8JH9P5BnTC68nXrqwh7XLF5UNodx5QMENpmql/ZFFWlPZGqO7P2ZmfbHD5wFnhtsbgEeBa8LxWz3ak3Wzmc00s3nuviutAqc9wFFug6laaJRapDVV28c4Ny/sXgHmhtvHAjvzzhsOxw4LRjNbQ1SrZMGCBRX98DQHOKq51FdSGqUWaU01D764u5uZlz/zsOetB9YD9Pf3V/z8tFR6qa9KaZRapPVUG4yv5prIZjYP2B2OjwDz887rDccyS7U6EYlLMvhSyEZgVbi9Crg/7/hlFlkGvJFm/2K9JB2sEZHOkGS6zh1EAy2zzWwY+CJwPXC3ma0GhoCV4fQHiabqbCOarnNFHcosIlJXSUalP13kobMKnOvA2loLJSLSTNU2pUVE2paCUUQkxqLWb5MLYbaHqK8yK2YDe5tdiCq1ctmhtcvfymWH1i5/sbIvdPc5lb5YJoIxa8xswN37m12OarRy2aG1y9/KZYfWLn/aZVdTWkQkRsEoIhKjYCxsfbMLUINWLju0dvlbuezQ2uVPtezqYxQRiVGNUUQkRsEoIhLTEcFoZt82s91m9mzesVPN7Gdm9gsz+76Z/VY43mdmb5rZ0+HrW3nPWRrO32Zm3wxbOWS+7GZ2hJn9u5m9aGbPmdn19S53muWPvd7G/NdqlfKb2QwzW29mW8Pv4cIWKvunw/nPmNkPzWx2vcteafnDY78THnsuPP72cLzyz627t/0X8CFgCfBs3rGngA+H258Fvhxu9+WfF3udJ4FlgAE/AFa0QtmBI4Dl4fYM4D8bUfY03/vw+AXA7aXOyWr5gb8FvhJudwGzW6HsRNdT2J0rL/A14G8y+N53A88Ap4b7s4Bp4XbFn9uG/HFl4Sv+iwfe4NDg03zg+TJ/IPOAF/Pufxr451Yoe4HXWwf8cau89+GxdwE/BU5qZDCmWP6dwDsbWe40yg5MB/YAC0OwfAtYk8HynwN8p8Dzq/rcdkRTuojniPaoAbiIqRfYPc7Mfm5mPzGz3w/HjiXaqiEnt21DM1Ra9klmNhP4JNEmZs1STfm/DHyd6HJ2zVZR+cN7DvBlM9tiZt81s7k0R0Vld/cDwJ8BvwB+RfQf0y0NLG9csfKfALiZ/Si8x58Px6v63HZyMH4W+HMzGwSOBMbC8V3AAnc/DbgauD2/HyMjqiq7mXUDdwDfdPftDS5zvorKb2bvB97r7vc1p7iHqfT97ya6mv1/ufsS4GfAPzS+2EDl7/10omA8DTiGqLn6hcYXe1Kx8ncDHwQuDd//0MwOuzRiUjXv+dKq3P1F4GwAMzsB+EQ4/hbwVrg9aGYvEf1vNEL0x53TtG0bqij7QHjqeuC/3f2Ghhc6TxXl/12g38x2EP3NHm1mj7r7mY0vfVXlHySq6X4vvMR3gdUNLjahXJWW3cKxl8Jz7ubQdskNV6z8RDXBx9x9b3jsQaL+ye9Qxee2Y2uMZnZ0+N4F/DVR3wlmNsfMpoXbxxPtkb3doy0a/sfMloVRrcs4tKVDpsse7n8FOAq4qhllzlfFe3+Tux/j7n1EtYGtzQrFULZKy+/A9zm05fBZwPMNLjahXJX+7YwAJ5lZ7go1HwNeaHS5c4qVH/gR8NsWzcDoBj5M1P9Y3ee20Z3Bzfgiaj7uAg4Q/c+yGvgcsDV8Xc+hDt0Lifoxnga2AJ/Me51+4FngJeCfcs/JetmJ/pd0oj/op8PXla303ue9Xh+NHZVO629nIfAYUVN0E1GztVXK/qfhb+cZooCflbX3Ppz/R+Hf8CzwtbzjFX9utSRQRCSmY5vSIiLFKBhFRGIUjCIiMQpGEZEYBaOISIyCUUQkRsEoIhLz/05TNaQpAd+fAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 360x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.io import loadmat\n",
    "\n",
    "data = np.load('airline.npz')\n",
    "\n",
    "X = data['X']\n",
    "y = data['y']\n",
    "\n",
    "train_indices = list(range(70)) + list(range(90, 129))\n",
    "test_indices = range(70, 90)\n",
    "X_train = X[train_indices]\n",
    "y_train = y[train_indices]\n",
    "\n",
    "X_test = X[test_indices]\n",
    "y_test = y[test_indices]\n",
    "\n",
    "plt.figure(figsize=(5, 3))\n",
    "plt.plot(X_train, y_train, '.')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You need to obtain something like this\n",
    "<img src=\"airline_result.png\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def plot_model(X, y, model):\n",
    "    x = np.linspace(1948, 1964, 400).reshape(-1, 1)\n",
    "    prediction_mean, prediction_var = model.predict(x)\n",
    "    prediction_std = np.sqrt(prediction_var).ravel()\n",
    "    prediction_mean = prediction_mean.ravel()\n",
    "    \n",
    "    plt.figure(figsize=(5, 3))\n",
    "    plt.plot(X, y, '.', label='Train data')\n",
    "    plt.plot(x, prediction_mean, label='Prediction')\n",
    "    plt.fill_between(x.ravel(), prediction_mean - prediction_std, prediction_mean + prediction_std, alpha=0.3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Let's try RBF kernel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "######## Your code here ########\n",
    "k_rbf = GPy.kern.RBF(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see below it doesn't work ;("
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Name : GP regression\n",
      "Objective : 695.9234946341753\n",
      "Number of Parameters : 3\n",
      "Number of Optimization Parameters : 3\n",
      "Updates : True\n",
      "Parameters:\n",
      "  \u001b[1mGP_regression.         \u001b[0;0m  |               value  |  constraints  |  priors\n",
      "  \u001b[1mrbf.variance           \u001b[0;0m  |   291074.8089397118  |      +ve      |        \n",
      "  \u001b[1mrbf.lengthscale        \u001b[0;0m  |  16.675774810483787  |      +ve      |        \n",
      "  \u001b[1mGaussian_noise.variance\u001b[0;0m  |   2471.691101460296  |      +ve      |        \n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = GPy.models.GPRegression(X, y, k_rbf)\n",
    "model.optimize()\n",
    "print(model)\n",
    "plot_model(X_train, y_train, model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "We will try to model this data set using 3 additive components: trend, seasonality and noise.  \n",
    "So, the kernel should be a sum of 3 kernels:  \n",
    "`kernel = kernel_trend + kernel_seasonality + kernel_noise`\n",
    "\n",
    "#### Let's first try to model trend\n",
    "\n",
    "Trend is almost linear with some small nonlinearity, so you can use sum of linear kernel with some other which gives this small nonlinearity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "######## Your code here ########\n",
    "k_trend = GPy.kern.Poly(1, order=1) + GPy.kern.RBF(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Name : GP regression\n",
      "Objective : 705.5389072606191\n",
      "Number of Parameters : 6\n",
      "Number of Optimization Parameters : 6\n",
      "Updates : True\n",
      "Parameters:\n",
      "  \u001b[1mGP_regression.         \u001b[0;0m  |               value  |  constraints  |  priors\n",
      "  \u001b[1msum.poly.variance      \u001b[0;0m  |   3366.052912739389  |      +ve      |        \n",
      "  \u001b[1msum.poly.scale         \u001b[0;0m  |   3365.143742324495  |      +ve      |        \n",
      "  \u001b[1msum.poly.bias          \u001b[0;0m  |   40.82859143415268  |      +ve      |        \n",
      "  \u001b[1msum.rbf.variance       \u001b[0;0m  |   54870.37549511879  |      +ve      |        \n",
      "  \u001b[1msum.rbf.lengthscale    \u001b[0;0m  |  11.550323699159936  |      +ve      |        \n",
      "  \u001b[1mGaussian_noise.variance\u001b[0;0m  |   2476.025964683786  |      +ve      |        \n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = GPy.models.GPRegression(X, y, k_trend)\n",
    "model.optimize()\n",
    "print(model)\n",
    "plot_model(X_train, y_train, model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Let's model periodicity\n",
    "Just periodic kernel will not work (why?).\n",
    "Try to use product of periodic kernel with some other kernel (or maybe 2 other kernels).\n",
    "Note that the amplitude increases with x."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "######## Your code here ########\n",
    "k_trend = GPy.kern.Poly(1, order=1) + GPy.kern.RBF(1)\n",
    "k_seasonal = GPy.kern.StdPeriodic(1) * GPy.kern.RBF(1) *  GPy.kern.Linear(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Name : GP regression\n",
      "Objective : 685.9234303480423\n",
      "Number of Parameters : 12\n",
      "Number of Optimization Parameters : 12\n",
      "Updates : True\n",
      "Parameters:\n",
      "  \u001b[1mGP_regression.                  \u001b[0;0m  |                value  |  constraints  |  priors\n",
      "  \u001b[1msum.poly.variance               \u001b[0;0m  |  0.19442236840627913  |      +ve      |        \n",
      "  \u001b[1msum.poly.scale                  \u001b[0;0m  |  0.19571819189021708  |      +ve      |        \n",
      "  \u001b[1msum.poly.bias                   \u001b[0;0m  |   0.9969959290950018  |      +ve      |        \n",
      "  \u001b[1msum.rbf.variance                \u001b[0;0m  |   139.46984407345877  |      +ve      |        \n",
      "  \u001b[1msum.rbf.lengthscale             \u001b[0;0m  |   125.36620466924145  |      +ve      |        \n",
      "  \u001b[1msum.mul.std_periodic.variance   \u001b[0;0m  |  0.14432346448299915  |      +ve      |        \n",
      "  \u001b[1msum.mul.std_periodic.period     \u001b[0;0m  |    0.432018338659004  |      +ve      |        \n",
      "  \u001b[1msum.mul.std_periodic.lengthscale\u001b[0;0m  |   1.8003610773878735  |      +ve      |        \n",
      "  \u001b[1msum.mul.rbf.variance            \u001b[0;0m  |  0.14432346439711277  |      +ve      |        \n",
      "  \u001b[1msum.mul.rbf.lengthscale         \u001b[0;0m  |   0.3700319878796113  |      +ve      |        \n",
      "  \u001b[1msum.mul.linear.variances        \u001b[0;0m  |  0.14432346429821613  |      +ve      |        \n",
      "  \u001b[1mGaussian_noise.variance         \u001b[0;0m  |    451.7620726717203  |      +ve      |        \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " /home/yeahrmek/miniconda3/lib/python3.6/site-packages/GPy/kern/src/stationary.py:167: RuntimeWarning:overflow encountered in true_divide\n",
      " /home/yeahrmek/miniconda3/lib/python3.6/site-packages/GPy/kern/src/rbf.py:43: RuntimeWarning:overflow encountered in square\n",
      " /home/yeahrmek/miniconda3/lib/python3.6/site-packages/GPy/kern/src/rbf.py:46: RuntimeWarning:invalid value encountered in multiply\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kernel = k_trend + k_seasonal\n",
    "model = GPy.models.GPRegression(X, y, kernel)\n",
    "model.optimize()\n",
    "print(model)\n",
    "plot_model(X_train, y_train, model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Let's add noise model\n",
    "The dataset is heteroscedastic, i.e. noise variance depends on x: it increases linearly with x.\n",
    "Noise can be modeled using `GPy.kern.White(1)`, but it assumes that noise variance is the same at every x.\n",
    "By what kernel it should be multiplied?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "######## Your code here ########\n",
    "k_trend = GPy.kern.Poly(1, order=1) + GPy.kern.RBF(1)\n",
    "k_periodicity = GPy.kern.StdPeriodic(1) * GPy.kern.RBF(1) * GPy.kern.Linear(1)\n",
    "k_noise = GPy.kern.White(1) * GPy.kern.Linear(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Name : GP regression\n",
      "Objective : 647.8976986990882\n",
      "Number of Parameters : 14\n",
      "Number of Optimization Parameters : 14\n",
      "Updates : True\n",
      "Parameters:\n",
      "  \u001b[1mGP_regression.                  \u001b[0;0m  |                 value  |  constraints  |  priors\n",
      "  \u001b[1msum.poly.variance               \u001b[0;0m  |   0.15095487889853598  |      +ve      |        \n",
      "  \u001b[1msum.poly.scale                  \u001b[0;0m  |   0.15097066976518084  |      +ve      |        \n",
      "  \u001b[1msum.poly.bias                   \u001b[0;0m  |    0.9999503270531906  |      +ve      |        \n",
      "  \u001b[1msum.rbf.variance                \u001b[0;0m  |    195.31494169461735  |      +ve      |        \n",
      "  \u001b[1msum.rbf.lengthscale             \u001b[0;0m  |    0.7594736297079168  |      +ve      |        \n",
      "  \u001b[1msum.mul.std_periodic.variance   \u001b[0;0m  |   0.21343301055724492  |      +ve      |        \n",
      "  \u001b[1msum.mul.std_periodic.period     \u001b[0;0m  |    1.0037690531138812  |      +ve      |        \n",
      "  \u001b[1msum.mul.std_periodic.lengthscale\u001b[0;0m  |    0.8090653620479369  |      +ve      |        \n",
      "  \u001b[1msum.mul.rbf.variance            \u001b[0;0m  |   0.21343301070572124  |      +ve      |        \n",
      "  \u001b[1msum.mul.rbf.lengthscale         \u001b[0;0m  |     9.307061735652233  |      +ve      |        \n",
      "  \u001b[1msum.mul.linear.variances        \u001b[0;0m  |   0.21343301074558804  |      +ve      |        \n",
      "  \u001b[1msum.mul_1.white.variance        \u001b[0;0m  |  0.014254164499210067  |      +ve      |        \n",
      "  \u001b[1msum.mul_1.linear.variances      \u001b[0;0m  |  0.014254164499091553  |      +ve      |        \n",
      "  \u001b[1mGaussian_noise.variance         \u001b[0;0m  |    0.8417615468234028  |      +ve      |        \n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kernel = k_trend + k_periodicity + k_noise\n",
    "model = GPy.models.GPRegression(X, y, kernel)\n",
    "model.optimize()\n",
    "print(model)\n",
    "plot_model(X_train, y_train, model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Automatic covariance structure search"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(7, 5));\n",
    "\n",
    "X = data['X']\n",
    "y = data['y']\n",
    "\n",
    "idx_test = np.where((X[:,0] > 1957))[0]\n",
    "idx_train = np.where((X[:,0] <= 1957))[0]\n",
    "X_train = X[idx_train]\n",
    "y_train = y[idx_train]\n",
    "\n",
    "X_test = X[idx_test]\n",
    "y_test = y[idx_test]\n",
    "\n",
    "plt.plot(X_train, y_train, '.', color='red');\n",
    "plt.plot(X_test, y_test, '.', color='green');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_model_learned(X, y, train_idx, test_idx, model):\n",
    "    prediction_mean, prediction_var = model.predict(X)\n",
    "    prediction_std = np.sqrt(prediction_var).ravel()\n",
    "    prediction_mean = prediction_mean.ravel()\n",
    "    \n",
    "    plt.figure(figsize=(7, 5))\n",
    "    plt.plot(X, y, '.')\n",
    "    plt.plot(X[train_idx], y[train_idx], '.', color='green')\n",
    "    plt.plot(X, prediction_mean, color='red')\n",
    "    plt.fill_between(X.ravel(), prediction_mean - prediction_std, prediction_mean + prediction_std, alpha=0.3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Expressing Sturcture Through Kernels"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For example:\n",
    "\n",
    "$$\n",
    "\\underbrace{\\text{RBF}\\times\\text{Lin}}_\\text{increasing trend} + \\underbrace{\\text{RBF}\\times\\text{Per}}_\\text{varying-amplitude periodic} + \\underbrace{\\text{RBF}}_\\text{residual}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Greedy Searching for the Optimum Kernel Combination"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One can wonder: how to automatically search the kernel structure? We can optimize some criteria, which balance between a loss function value and the complexity of the model.\n",
    "Reasinobale candidate for this is BIC-criteria:\n",
    "\n",
    "$$\n",
    "BIC = - 2. \\text{Log-Liklihood} + m \\cdot\\log{n}\n",
    "$$\n",
    "\n",
    "where $n$ sample size and $m$ number of the parameters.\n",
    "\n",
    "However, the procedure of fitting Gaussian Process is quite expensive $O(n^3)$. Hence,  instead of the combinatorial search through all possible combinations, we grow the kernel structure greedy.\n",
    "\n",
    "You can find more details at the https://github.com/jamesrobertlloyd/gp-structure-search. For now, we present toy-example algorithm."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider the set of operations:\n",
    "\n",
    "$$\n",
    "\\text{Algebra: } +,\\times\n",
    "$$\n",
    "\n",
    "and the set of basic kernels:\n",
    "\n",
    "$$\n",
    "\\text{Kernels: } \\text{Poly}, \\text{RBF}, \\text{Periodic}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For each level we select extenstion of our current kernel with the lowest BIC. This is an example of the possible kernel grow process (mark notes the lowest BIC at the level):"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src='gp.png'>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train_model_get_bic(X_train, y_train, kernel, num_restarts=3):\n",
    "    '''\n",
    "    Input:\n",
    "        X_train: numpy array of train features, n*d (d>=1)\n",
    "        y_train: numpy array n*1\n",
    "        kernel: GPy object kern\n",
    "        num_restars: number of the restarts of the optimization routine\n",
    "    Output:\n",
    "        bic value\n",
    "    '''\n",
    "    kernel = kernel.copy()\n",
    "    model = GPy.models.GPRegression(X_train, y_train, kernel, None)\n",
    "    model.optimize_restarts(num_restarts, verbose=False)\n",
    "    \n",
    "    log_ll = model.log_likelihood()\n",
    "    N = X_train.shape[0]\n",
    "    m = model.param_array.shape[0]\n",
    "    bic = -2.*log_ll + m * np.log(N)\n",
    "    \n",
    "    return bic "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "def _make_all_products(op_list, kernel_list):\n",
    "    '''\n",
    "    Find product pairs\n",
    "    '''\n",
    "    product_index = np.where(np.array(op_list) == '*')[0]\n",
    "    if len(product_index) == 0:\n",
    "        return kernel_list\n",
    "\n",
    "    product_index = product_index[0]\n",
    "    product_kernel = kernel_list[product_index] * kernel_list[product_index + 1]\n",
    "    \n",
    "    if len(op_list) == product_index + 1:\n",
    "        kernel_list_copy = kernel_list[:product_index] + [product_kernel]\n",
    "        op_list_copy = op_list[:product_index]\n",
    "    else:\n",
    "        kernel_list_copy = kernel_list[:product_index] + [product_kernel] + kernel_list[product_index + 2:]\n",
    "        op_list_copy = op_list[:product_index] + op_list[product_index + 1:]\n",
    "        \n",
    "    return _make_all_products(op_list_copy, kernel_list_copy)\n",
    "\n",
    "\n",
    "class GreedyKernel:\n",
    "    '''\n",
    "    Class for greedy growing kernel structure\n",
    "    '''\n",
    "    def __init__(self, algebra, base_kernels):\n",
    "        self.algebra = algebra\n",
    "        self.base_kernels = base_kernels\n",
    "        self.kernel = None\n",
    "        self.kernel_list = []\n",
    "        self.op_list = []\n",
    "        self.str_kernel = None\n",
    "    \n",
    "    def _make_kernel(self, op_list, kernel_list):\n",
    "        '''\n",
    "        Sumation in kernel experssion\n",
    "        '''\n",
    "        kernels_to_sum = _make_all_products(op_list, kernel_list)\n",
    "        new_kernel = kernels_to_sum[0]\n",
    "        for k in kernels_to_sum[1:]:\n",
    "            new_kernel = new_kernel + k\n",
    "        return new_kernel\n",
    "    \n",
    "    def init_kernel(self, X_train, y_train):\n",
    "        '''\n",
    "        Initialization of first kernel\n",
    "        '''\n",
    "        bic = np.zeros(len(self.base_kernels))\n",
    "        for k, kernel in enumerate(self.base_kernels):\n",
    "            bic[k] = train_model_get_bic(X_train, y_train, kernel)\n",
    "        self.kernel = self.base_kernels[np.argmin(bic)]\n",
    "        self.kernel_list.append(self.kernel.copy())\n",
    "        self.str_kernel = str(self.kernel.name)\n",
    "        \n",
    "    def grow_level(self, X_train, y_train):\n",
    "        '''\n",
    "        Select optimal extension of current kernel \n",
    "        '''    \n",
    "        best_bic = np.inf\n",
    "        best_op, best_kernel = None, None\n",
    "        \n",
    "        for k, kernel in enumerate(self.base_kernels):\n",
    "            for a, (op_name, op) in enumerate(self.algebra.items()):\n",
    "                new_kernel = self._make_kernel(self.op_list + [op_name], self.kernel_list + [kernel])\n",
    "                bic = train_model_get_bic(X_train, y_train, new_kernel)\n",
    "                if bic < best_bic:\n",
    "                    best_op = op_name\n",
    "                    best_kernel = kernel\n",
    "                    best_bic = bic\n",
    "                \n",
    "        self.kernel_list.append(best_kernel.copy())\n",
    "        self.op_list.append(best_op)\n",
    "        \n",
    "        new_kernel = self._make_kernel(self.op_list, self.kernel_list)\n",
    "        str_new_kernel = '{} {} {}'.format(self.str_kernel, best_op, best_kernel.name)\n",
    "        \n",
    "        return new_kernel, str_new_kernel\n",
    "    \n",
    "    def grow_tree(self, X_train, y_train, max_depth):\n",
    "        '''\n",
    "        Greedy kernel growing\n",
    "        '''\n",
    "        if self.kernel == None:\n",
    "            self.init_kernel(X_train, y_train)\n",
    "            \n",
    "        for i in range(max_depth):\n",
    "            self.kernel, self.str_kernel = self.grow_level(X_train, y_train)\n",
    "            print(self.str_kernel)\n",
    "            \n",
    "    def fit_model(self, X_train, y_train, kernel, num_restarts=1):\n",
    "        model = GPy.models.GPRegression(X_train, y_train, kernel)\n",
    "        model.optimize_restarts(num_restarts, verbose=False)\n",
    "        return model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "reconstraining parameters std_periodic.period\n",
      "reconstraining parameters std_periodic.lengthscale\n",
      "reconstraining parameters rbf.lengthscale\n"
     ]
    }
   ],
   "source": [
    "# operations under kernels:\n",
    "\n",
    "algebra = {'+': lambda x, y: x + y,\n",
    "           '*': lambda x, y: x * y\n",
    "          }\n",
    "\n",
    "# basic kernels list:\n",
    "\n",
    "poly_kern = GPy.kern.Poly(input_dim=1, order=1)\n",
    "\n",
    "periodic_kern = GPy.kern.StdPeriodic(input_dim=1)\n",
    "periodic_kern.period.constrain_bounded(1e-2, 1e1)\n",
    "periodic_kern.lengthscale.constrain_bounded(1e-2, 1e1)\n",
    "\n",
    "rbf_kern = GPy.kern.RBF(input_dim=1)\n",
    "rbf_kern.lengthscale.constrain_bounded(1e-2, 1e1)\n",
    "\n",
    "bias_kern = GPy.kern.Bias(1)\n",
    "\n",
    "kernels_list = [poly_kern, periodic_kern, rbf_kern]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The algorithm is not perfect, but still it returns something reasonable.  \n",
    "In order to improve it you can think of more advanced greed strategy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " /home/yeahrmek/miniconda3/lib/python3.6/site-packages/ipykernel_launcher.py:5: FutureWarning:elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rbf + rbf\n",
      "rbf + rbf * std_periodic\n",
      "rbf + rbf * std_periodic + rbf\n",
      "rbf + rbf * std_periodic + rbf * std_periodic\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "GK = GreedyKernel(algebra, kernels_list)\n",
    "GK.grow_tree(X_train, y_train, 4)\n",
    "model = GK.fit_model(X_train, y_train, GK.kernel)\n",
    "plot_model_learned(X, y, idx_train, idx_test, model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Appendix: Gaussian Process Classification"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Classification\n",
    "\n",
    "A data set $\\left (X, \\mathbf{y} \\right ) = \\left \\{ (x_i, y_i), x_i \\in \\mathbb{R}^d, y_i \\in \\{+1, -1\\} \\right \\}_{i = 1}^N$ is given.  \n",
    "\n",
    "Assumption:\n",
    "$$\n",
    "p(y = +1 \\; | \\; x) = \\sigma(f(x)) = \\pi(x),\n",
    "$$\n",
    "where latent function $f(x)$ is a Gaussian Processes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "We need to produce a probabilistic prediction\n",
    "$$\n",
    "\\pi_* = p(y_* \\; | \\; X, \\mathbf{y}, x_*) = \\int \\sigma(f_*) p(f_* \\; | \\; X, \\mathbf{y}, x_*) df_*,\n",
    "$$\n",
    "$$\n",
    "p(f_* \\; | \\; X, \\mathbf{y}, x_*) = \\int p(f_* \\; | \\; X, x_*, \\mathbf{f}) p(\\mathbf{f} \\; | \\; X, \\mathbf{y}) d\\mathbf{f},\n",
    "$$\n",
    "where $p(\\mathbf{f} \\; |\\; X, \\mathbf{y}) = \\dfrac{p(\\mathbf{y} | X, \\mathbf{f}) p(\\mathbf{f} | X)}{p(\\mathbf{y} | X)}$ is the posterior over the latent variables.\n",
    "\n",
    "Both integrals are intractable.\n",
    "\n",
    "Use approximation technique like Laplace approximation or Expectation Propagation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "from matplotlib import cm\n",
    "\n",
    "def cylinder(x):\n",
    "    y = (1 / 7.0 - (x[:, 0] - 0.5)**2 - (x[:, 1] - 0.5)**2) > 0\n",
    "    return y\n",
    "\n",
    "np.random.seed(42)\n",
    "X = np.random.rand(40, 2)\n",
    "y = cylinder(X)\n",
    "\n",
    "x_grid = np.meshgrid(np.linspace(0, 1, 100), np.linspace(0, 1, 100))\n",
    "y_grid = cylinder(np.hstack((x_grid[0].reshape(-1, 1), x_grid[1].reshape(-1, 1)))).reshape(x_grid[0].shape)\n",
    "\n",
    "positive_idx = y == 1\n",
    "plt.figure(figsize=(5, 3))\n",
    "plt.plot(X[positive_idx, 0], X[positive_idx, 1], '.', markersize=10, label='Positive')\n",
    "plt.plot(X[~positive_idx, 0], X[~positive_idx, 1], '.', markersize=10, label='Negative')\n",
    "im = plt.contour(x_grid[0], x_grid[1], y_grid, 10, cmap=cm.hot)\n",
    "plt.colorbar(im)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "kernel = GPy.kern.RBF(2, variance=1., lengthscale=0.2, ARD=True)\n",
    "\n",
    "model = GPy.models.GPClassification(X, y.reshape(-1, 1), kernel=kernel)\n",
    "model.optimize()\n",
    "print(model)\n",
    "\n",
    "\n",
    "def plot_model_2d(model):\n",
    "\n",
    "    model.plot(levels=40, resolution=80, plot_data=False, figsize=(5, 3))\n",
    "    plt.plot(X[positive_idx, 0], X[positive_idx, 1], '.', markersize=10, label='Positive')\n",
    "    plt.plot(X[~positive_idx, 0], X[~positive_idx, 1], '.', markersize=10, label='Negative')\n",
    "    plt.legend()\n",
    "    plt.show()\n",
    "    \n",
    "plot_model_2d(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's change lengthscale to some small value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "model.rbf.lengthscale = [0.05, 0.05]\n",
    "plot_model_2d(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bonus Task\n",
    "Try to approximate rastrigin function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig = plot_2d_func(rastrigin)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.rand(42)\n",
    "x_train = np.random.rand(200, 2)\n",
    "y_train = rastrigin(x_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Hint: you can constrain parameters of the covariance functions, for example\n",
    "`model.std_periodic.period.constrain_bounded(0, 0.2)`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "######## Your code here ########\n",
    "kernel = GPy.kern.RBF(2) * GPy.kern.StdPeriodic(2)\n",
    "model = GPy.models.GPRegression(x_train, y_train.reshape(-1, 1), kernel)\n",
    "# model.Gaussian_noise.variance.constrain_bounded(0, 0.01)\n",
    "model.mul.std_periodic.period.constrain_bounded(0, 0.2)\n",
    "model.optimize_restarts(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(model)\n",
    "\n",
    "x_test = np.random.rand(1000, 2)\n",
    "y_test = rastrigin(x_test)\n",
    "y_pr = model.predict(x_test)[0]\n",
    "\n",
    "mse = mean_squared_error(y_test.ravel(), y_pr.ravel())\n",
    "print('MSE: {}'.format(mse))\n",
    "\n",
    "fig = plot_2d_func(lambda x: model.predict(x)[0])"
   ]
  }
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